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  • ON SOLVABILITY OF CERTAIN EQUATIONS OF ARBITRARY LENGTH OVER TORSION-FREE GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-10-13
    MUHAMMAD FAZEEL ANWAR; MAIRAJ BIBI; MUHAMMAD SAEED AKRAM

    Let G be a nontrivial torsion-free group and $s\left( t \right) = {g_1}{t^{{\varepsilon _1}}}{g_2}{t^{{\varepsilon _2}}} \ldots {g_n}{t^{{\varepsilon _n}}} = 1\left( {{g_i} \in G,{\varepsilon_i} = \pm 1} \right)$ be an equation over G containing no blocks of the form ${t^{- 1}}{g_i}{t^{ - 1}},{g_i} \in G$ . In this paper, we show that $s\left( t \right) = 1$ has a solution over G provided a single

    更新日期:2020-10-13
  • A GENERALIZATION OF THE THEORY OF STANDARDLY STRATIFIED ALGEBRAS I: STANDARDLY STRATIFIED RINGOIDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-10-07
    O. MENDOZA; M. ORTÍZ; C. SÁENZ; V. SANTIAGO

    We extend the classical notion of standardly stratified k-algebra (stated for finite dimensional k-algebras) to the more general class of rings, possibly without 1, with enough idempotents. We show that many of the fundamental results, which are known for classical standardly stratified algebras, can be generalized to this context. Furthermore, new classes of rings appear as: ideally standardly stratified

    更新日期:2020-10-07
  • D3-MODULES VERSUS D4-MODULES – APPLICATIONS TO QUIVERS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-10-06
    GABRIELLA D′ESTE; DERYA KESKİN TÜTÜNCÜ; RACHID TRIBAK

    A module M is called a D4-module if, whenever A and B are submodules of M with M = A ⊕ B and f : A → B is a homomorphism with Imf a direct summand of B, then Kerf is a direct summand of A. The class of D4-modules contains the class of D3-modules, and hence the class of semi-projective modules, and so the class of Rickart modules. In this paper we prove that, over a commutative Dedekind domain R, for

    更新日期:2020-10-06
  • CONGRUENCE PRIMES FOR SIEGEL MODULAR FORMS OF PARAMODULAR LEVEL AND APPLICATIONS TO THE BLOCH–KATO CONJECTURE
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-09-29
    JIM BROWN; HUIXI LI

    It has been well established that congruences between automorphic forms have far-reaching applications in arithmetic. In this paper, we construct congruences for Siegel–Hilbert modular forms defined over a totally real field of class number 1. As an application of this general congruence, we produce congruences between paramodular Saito–Kurokawa lifts and non-lifted Siegel modular forms. These congruences

    更新日期:2020-09-29
  • REAL HYPERSURFACES IN COMPLEX SPACE FORMS ATTAINING EQUALITY IN AN INEQUALITY INVOLVING A CONTACT δ-INVARIANT
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-09-24
    TORU SASAHARA

    We investigate real hypersurfaces in nonflat complex space forms attaining equality in an inequality involving the contact δ-invariant δc(2) introduced by Chen and Mihai in [3].

    更新日期:2020-09-24
  • SPECTRAL CONDITIONS FOR UNIFORM P-ERGODICITIES OF MARKOV OPERATORS ON ABSTRACT STATES SPACES
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-09-23
    NAZIFE ERKURŞUN-ÖZCAN; FARRUKH MUKHAMEDOV

    In the present paper, we deal with asymptotical stability of Markov operators acting on abstract state spaces (i.e. an ordered Banach space, where the norm has an additivity property on the cone of positive elements). Basically, we are interested in the rate of convergence when a Markov operator T satisfies the uniform P-ergodicity, i.e. $\|T^n-P\|\to 0$ , here P is a projection. We have showed that

    更新日期:2020-09-24
  • FINITE GROUPS WITH THE SAME JOIN GRAPH AS A FINITE NILPOTENT GROUP
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-17
    ANDREA LUCCHINI

    Given a finite group G, we denote by Δ(G) the graph whose vertices are the proper subgroups of G and in which two vertices H and K are joined by an edge if and only if G = ⟨H, K⟩. We prove that if there exists a finite nilpotent group X with Δ(G) ≅ Δ(X), then G is supersoluble.

    更新日期:2020-08-17
  • VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-17
    MOHSEN KIAN; MOHAMMAD SAL MOSLEHIAN; YUKI SEO

    For an n-tuple of positive invertible operators on a Hilbert space, we present some variants of Ando–Hiai type inequalities for deformed means from an n-variable operator mean by an operator mean, which is related to the information monotonicity of a certain unital positive linear map. As an application, we investigate the monotonicity of the power mean from the deformed mean in terms of the generalized

    更新日期:2020-08-17
  • LINEAR RELATIONS AND INTEGRABILITY FOR CLUSTER ALGEBRAS FROM AFFINE QUIVERS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-13
    JOE PALLISTER

    We consider frieze sequences corresponding to sequences of cluster mutations for affine D- and E-type quivers. We show that the cluster variables satisfy linear recurrences with periodic coefficients, which imply the constant coefficient relations found by Keller and Scherotzke. Viewing the frieze sequence as a discrete dynamical system, we reduce it to a symplectic map on a lower dimensional space

    更新日期:2020-08-14
  • A NOTE ON p-ADIC SIMPLICIAL VOLUMES
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-13
    STEFFEN KIONKE; CLARA LÖH

    We define and study generalizations of simplicial volume over arbitrary seminormed rings with a focus on p-adic simplicial volumes. We investigate the dependence on the prime and establish homology bounds in terms of p-adic simplicial volumes. As the main examples, we compute the weightless and p-adic simplicial volumes of surfaces. This is based on an alternative way to calculate classical simplicial

    更新日期:2020-08-14
  • AN INVARIANT OF LEGENDRIAN AND TRANSVERSE LINKS FROM OPEN BOOK DECOMPOSITIONS OF CONTACT 3-MANIFOLDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-04
    ALBERTO CAVALLO

    We introduce a generalization of the Lisca–Ozsváth–Stipsicz–Szabó Legendrian invariant ${\mathfrak L}$ to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link L in a contact 3-manifold ${(M,\xi)}$ with a diagram D, given by an open book decomposition of ${(M,\xi)}$ adapted to L, and we construct a chain complex ${cCFL^-(D)}$ with

    更新日期:2020-08-04
  • THE CASIMIR NUMBER AND THE DETERMINANT OF A FUSION CATEGORY
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-04
    ZHIHUA WANG; GONGXIANG LIU; LIBIN LI

    Let $\mathcal{C}$ be a fusion category over an algebraically closed field $\mathbb{k}$ of arbitrary characteristic. Two numerical invariants of $\mathcal{C}$ , that is, the Casimir number and the determinant of $\mathcal{C}$ are considered in this paper. These two numbers are both positive integers and admit the property that the Grothendieck algebra $(\mathcal{C})\otimes_{\mathbb{Z}}K$ over any field

    更新日期:2020-08-04
  • GENERALISED QUANTUM DETERMINANTAL RINGS ARE MAXIMAL ORDERS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-04
    T. H. LENAGAN; L. RIGAL

    Generalised quantum determinantal rings are the analogue in quantum matrices of Schubert varieties. Maximal orders are the noncommutative version of integrally closed rings. In this paper, we show that generalised quantum determinantal rings are maximal orders. The cornerstone of the proof is a description of generalised quantum determinantal rings, up to a localisation, as skew polynomial extensions

    更新日期:2020-08-04
  • THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPE A
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-29
    JORDAN MCMAHON; NICHOLAS J. WILLIAMS

    We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective

    更新日期:2020-07-29
  • ON GILP’S GROUP-THEORETIC APPROACH TO FALCONER’S DISTANCE PROBLEM
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-28
    HAN YU

    In this paper, we follow and extend a group-theoretic method introduced by Greenleaf–Iosevich–Liu–Palsson (GILP) to study finite points configurations spanned by Borel sets in $\mathbb{R}^n,n\geq 2,n\in\mathbb{N}.$ We remove a technical continuity condition in a GILP’s theorem in [Revista Mat. Iberoamer31 (2015), 799–810]. This allows us to extend the Wolff–Erdogan dimension bound for distance sets

    更新日期:2020-07-28
  • REDUCTIONS OF POINTS ON ALGEBRAIC GROUPS, II
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-28
    PETER BRUIN; ANTONELLA PERUCCA

    Let A be the product of an abelian variety and a torus over a number field K, and let $$m \ge 2$$ be a square-free integer. If $\alpha \in A(K)$ is a point of infinite order, we consider the set of primes $\mathfrak p$ of K such that the reduction $(\alpha \bmod \mathfrak p)$ is well defined and has order coprime to m. This set admits a natural density, which we are able to express as a finite sum

    更新日期:2020-07-28
  • PRIME AND SEMIPRIME QUANTUM LINEAR SPACE SMASH PRODUCTS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-23
    JASON GADDIS

    Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum linear space to be (semi)prime. These are then used to determine (semi)primeness of certain smash products with quantum affine spaces. This extends Bergen’s work

    更新日期:2020-07-23
  • DUALIZING INVOLUTIONS ON THE METAPLECTIC GL(2) à la TUPAN
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-10
    KUMAR BALASUBRAMANIAN; EKTA TIWARI

    Let F be a non-Archimedean local field of characteristic zero. Let G = GL(2, F) and $3\widetildeG = \widetilde{GL}(2,F)$ be the metaplectic group. Let τ be the standard involution on G. A well-known theorem of Gelfand and Kazhdan says that the standard involution takes any irreducible admissible representation of G to its contragredient. In such a case, we say that τ is a dualizing involution. In this

    更新日期:2020-07-10
  • CLOSED IDEALS AND LIE IDEALS OF MINIMAL TENSOR PRODUCT OF CERTAIN C*-ALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-03
    BHARAT TALWAR; RANJANA JAIN

    For a locally compact Hausdorff space X and a C*-algebra A with only finitely many closed ideals, we discuss a characterization of closed ideals of C0(X,A) in terms of closed ideals of A and a class of closed subspaces of X. We further use this result to prove that a closed ideal of C0(X)⊗minA is a finite sum of product ideals. We also establish that for a unital C*-algebra A, C0(X,A) has the centre-quotient

    更新日期:2020-07-03
  • CYCLIC BRANCHED COVERINGS OF BRIESKORN SPHERES BOUNDING ACYCLIC 4-MANIFOLDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-03
    NIMA ANVARI; IAN HAMBLETON

    We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic 4-manifold with boundary a related Brieskorn homology sphere. We briefly discuss well-known invariants of homology spheres that obstruct acyclic bounding 4-manifolds and then use

    更新日期:2020-07-03
  • POTENTIAL ALGEBRAS WITH FEW GENERATORS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-01
    NATALIA IYUDU; STANISLAV SHKARIN

    We give a complete description of quadratic twisted potential algebras on three generators as well as cubic twisted potential algebras on two generators up to graded algebra isomorphisms under the assumption that the ground field is algebraically closed and has characteristic other than 2 or 3.

    更新日期:2020-07-01
  • A FAST ALGORITHM FOR CALCULATING S-INVARIANTS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-06-29
    DIRK SCHÜTZ

    We use the divide-and-conquer and scanning algorithms for calculating Khovanov cohomology directly on the Lee- or Bar-Natan deformations of the Khovanov complex to give an alternative way to compute Rasmussen s-invariants of knots. By disregarding generators away from homological degree 0, we can considerably improve the efficiency of the algorithm. With a slight modification, we can also apply it

    更新日期:2020-06-29
  • DISTAL ACTIONS OF AUTOMORPHISMS OF NILPOTENT GROUPS G ON SUBG AND APPLICATIONS TO LATTICES IN LIE GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-06-23
    RAJDIP PALIT; RIDDHI SHAH

    For a locally compact group G, we study the distality of the action of automorphisms T of G on SubG, the compact space of closed subgroups of G endowed with the Chabauty topology. For a certain class of discrete groups G, we show that T acts distally on SubG if and only if Tn is the identity map for some $n\in\mathbb N$ . As an application, we get that for a T-invariant lattice Γ in a simply connected

    更新日期:2020-06-23
  • NONHYPERELLIPTIC FIBRATIONS OF GENUS 4 WITH NONSURJECTIVE MULTIPLICATION MAP
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-06-15
    TOMOKUNI TAKAHASHI

    We prove some numerical inequality for the Horikawa indices for Eisenbud–Harris special nonhyperelliptic fibrations of genus 4 on algebraic surfaces under the assumption that the multiplication map of the fibration is not surjective. Furthermore, we prove that the inequality is best possible by constructing the examples satisfying the equality.

    更新日期:2020-06-15
  • DETECTING STEINER AND LINEAR ISOMETRIES OPERADS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-19
    JONATHAN RUBIN

    We study the indexing systems that correspond to equivariant Steiner and linear isometries operads. When G is a finite abelian group, we prove that a G-indexing system is realized by a Steiner operad if and only if it is generated by cyclic G-orbits. When G is a finite cyclic group, whose order is either a prime power or a product of two distinct primes greater than 3, we prove that a G-indexing system

    更新日期:2020-05-19
  • ISOTOPY AND HOMEOMORPHISM OF CLOSED SURFACE BRAIDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-15
    MARK GRANT; AGATA SIENICKA

    The closure of a braid in a closed orientable surface Ʃ is a link in Ʃ × S1. We classify such closed surface braids up to isotopy and homeomorphism (with a small indeterminacy for isotopy of closed sphere braids), algebraically in terms of the surface braid group. We find that in positive genus, braids close to isotopic links if and only if they are conjugate, and close to homeomorphic links if and

    更新日期:2020-05-15
  • A NOTE ON CHAINS AND BOUNDING PAIRS OF DEHN TWISTS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-15
    FERIHE ATALAN

    Let $N_g^k$ be a nonorientable surface of genus g with k punctures. In the first part of this note, after introducing preliminary materials, we will give criteria for a chain of Dehn twists to bound a disc. Then, we will show that automorphisms of the mapping class groups map disc bounding chains of Dehn twists to such chains. In the second part of the note, we will introduce bounding pairs of Dehn

    更新日期:2020-05-15
  • AN EXTENSION OF A RESULT OF ERDŐS AND ZAREMBA
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-13
    MICHEL JEAN GEORGES WEBER

    Erdös and Zaremba showed that $ \limsup_{n\to \infty} \frac{\Phi(n)}{(\log\log n)^2}=e^\gamma$ , γ being Euler’s constant, where $\Phi(n)=\sum_{d|n} \frac{\log d}{d}$ .

    更新日期:2020-05-13
  • PRIMITIVE RECURSIVE DECIDABILITY FOR THE RING OF INTEGERS OF THE COMPOSITUM OF ALL SYMMETRIC EXTENSIONS OF ℚ
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-08
    MOSHE JARDEN; AHARON RAZON

    Let ℚsymm be the compositum of all symmetric extensions of ℚ, i.e., the finite Galois extensions with Galois group isomorphic to Sn for some positive integer n, and let ℤsymm be the ring of integers inside ℚsymm. Then, TH(ℤsymm) is primitive recursively decidable.

    更新日期:2020-05-08
  • NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-07
    IGNACIO F. RÚA

    Symplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters $(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$ over a Galois field of order $q=2^l$ , for all $0\le r\le\frac{m-1}{2}$

    更新日期:2020-05-07
  • HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-27
    MICHAEL J. CRABB; JOHN DUNCAN; COLIN M. McGREGOR

    We investigate the real space H of Hermitian matrices in $M_n(\mathbb{C})$ with respect to norms on $\mathbb{C}^n$ . For absolute norms, the general form of Hermitian matrices was essentially established by Schneider and Turner [Schneider and Turner, Linear and Multilinear Algebra (1973), 9–31]. Here, we offer a much shorter proof. For non-absolute norms, we begin an investigation of H by means of

    更新日期:2020-04-27
  • ON SOME QUESTIONS OF PARTITIO NUMERORUM: TRES CUBI
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-21
    R. C. VAUGHAN

    This paper is concerned with the function r3(n), the number of representations of n as the sum of at most three positive cubes, $$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$ , Our understanding of this function is surprisingly poor, and we examine various averages of it. In particular $${\sum_{m=1}^nr_3(m),\,\sum_{m=1}^nr_3(m)^2}$$ and $${\sum_{\substack{ n\le

    更新日期:2020-04-21
  • BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-20
    GENQIANG LIU; YANG LI

    In 1996, a q-deformation of the universal enveloping algebra of the Schrödinger Lie algebra was introduced in Dobrev et al. [J. Phys. A 29 (1996) 5909–5918.]. This algebra is called the quantum Schrödinger algebra. In this paper, we study the Bernstein-Gelfand-Gelfand (BGG) category $\mathcal{O}$ for the quantum Schrödinger algebra $U_q(\mathfrak{s})$ , where q is a nonzero complex number which is

    更新日期:2020-04-20
  • ANNIHILATOR-STABILITY AND TWO QUESTIONS OF NICHOLSON
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-07
    GUOLI XIA; YIQIANG ZHOU

    An element a in a ring R is left annihilator-stable (or left AS) if, whenever $Ra+{\rm l}(b)=R$ with $b\in R$ , $a-u\in {\rm l}(b)$ for a unit u in R, and the ring R is a left AS ring if each of its elements is left AS. In this paper, we show that the left AS elements in a ring form a multiplicatively closed set, giving an affirmative answer to a question of Nicholson [J. Pure Appl. Alg.221 (2017)

    更新日期:2020-04-07
  • ON THE EIGENVALUES AND THE NODAL POINTS OF THE EIGENFUNCTIONS OF SOME EIGENVALUE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-07
    CHI-HUA CHAN; PO-CHUN HUANG

    Consider the following two eigenvalue problems: (0.1) \begin{cases}\label{eqn:1abs}y"(x)+[\lambda^2-q(x)]y(x)=0, 0 \leq x \leq \pi,\\[3pt] y(0)=0, ay'(\pi)+\lambda y(\pi)=0, \end{cases} and (0.2) \begin{cases} z"(x)+[\mu^2-q(x)]z(x)=0, 0 \leq x \leq \pi,\\[3pt] z'(0)=0, az'(\pi)+\mu z(\pi)=0, \end{cases}

    更新日期:2020-04-07
  • FOUR-MANIFOLDS WITH POSITIVE CURVATURE
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-06
    R. DIÓGENES; E. RIBEIRO; E. RUFINO

    In this note, we prove that a four-dimensional compact oriented half-conformally flat Riemannian manifold M4 is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2}$ , provided that the sectional curvatures all lie in the interval $\left[ {{{3\sqrt {3 - 5} } \over 4}, 1} \right]$ In addition, we use the notion of biorthogonal (sectional) curvature to obtain a pinching condition which guarantees

    更新日期:2020-04-06
  • (WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-16
    ULRICH KRÄHMER; LUCIA ROTHERAY

    Incidence coalgebras of categories in the sense of Joni and Rota are studied, specifically cases where a monoidal product on the category turns these into (weak) bialgebras. The overlap with the theory of combinatorial Hopf algebras and that of Hopf quivers is discussed, and examples including trees, skew shapes, Milner’s bigraphs and crossed modules are considered.

    更新日期:2020-03-16
  • FRACTIONAL SCHRÖDINGER–POISSON SYSTEM WITH SINGULARITY: EXISTENCE, UNIQUENESS, AND ASYMPTOTIC BEHAVIOR
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-12
    SHENGBIN YU; JIANQING CHEN

    In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*}

    更新日期:2020-03-12
  • WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-12
    BOUALEM BENSEBAA; ABBAS MOVAHHEDI; ALAIN SALINIER

    It is proven that, for a wide range of integers s (2 < s < p − 2), the existence of a single wildly ramified odd prime l ≠ p leads to either the alternating group or the full symmetric group as Galois group of any irreducible trinomial Xp + aXs + b of prime degree p.

    更新日期:2020-03-12
  • ON THE σ-NILPOTENT NORM AND THE σ-NILPOTENT LENGTH OF A FINITE GROUP
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-27
    BIN HU; JIANHONG HUANG; ALEXANDER N. SKIBA

    Let G be a finite group and σ = {σi| i ∈ I} some partition of the set of all primes $\Bbb{P}$ . Then G is said to be: σ-primary if G is a σi-group for some i; σ-nilpotent if G = G1× … × Gt for some σ-primary groups G1, … , Gt; σ-soluble if every chief factor of G is σ-primary. We use $G^{{\mathfrak{N}}_{\sigma}}$ to denote the σ-nilpotent residual of G, that is, the intersection of all normal subgroups

    更新日期:2020-02-27
  • FINITENESS OF TOPOLOGICAL ENTROPY FOR LOCALLY COMPACT ABELIAN GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-26
    DIKRAN DIKRANJAN; ANNA GIORDANO BRUNO; FRANCESCO G. RUSSO

    We study the locally compact abelian groups in the class ${\mathfrak E_{ \lt \infty }}$ , that is, having only continuous endomorphisms of finite topological entropy, and in its subclass $\mathfrak E_0$ , that is, having all continuous endomorphisms with vanishing topological entropy. We discuss the reduction of the problem to the case of periodic locally compact abelian groups, and then to locally

    更新日期:2020-02-26
  • GENERALIZED FINITE POLYLOGARITHMS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-19
    MARINA AVITABILE; SANDRO MATTAREI

    We introduce a generalization ${\rm{\pounds}}_d^{(\alpha)}(X)$ of the finite polylogarithms ${\rm{\pounds}}_d^{(0)}(X) = {{\rm{\pounds}}_d}(X) = \sum\nolimits_{k = 1}^{p - 1} {X^k}/{k^d}$ , in characteristic p, which depends on a parameter α. The special case ${\rm{\pounds}}_1^{(\alpha)}(X)$ was previously investigated by the authors as the inverse, in an appropriate sense, of a parametrized generalization

    更新日期:2020-02-19
  • GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-03
    DUNCAN MCCOY

    For p ≥ 1, one can define a generalisation of the unknotting number tup called the pth untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tup–1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large

    更新日期:2020-02-03
  • POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-01-10
    OLGUR CELIKBAS; RYO TAKAHASHI

    We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid and strongly rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion condition of a long-standing conjecture of Huneke and Wiegand.

    更新日期:2020-01-10
  • ON FINITE-BY-NILPOTENT GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-20
    ELOISA DETOMI; GURAM DONADZE; MARTA MORIGI; PAVEL SHUMYATSKY

    Let γn = [x1,…,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that $|{g^{{X_n}}}| \le m$ for each g ∈ G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.

    更新日期:2019-12-20
  • THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-12
    LEONID CHAICHENETS; NIKOLAOS PATTAKOS

    We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces ${M}^s_{p,q}(\mathbb{R}^d)$ , where q = 1 and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities.

    更新日期:2019-12-12
  • HOMOLOGY THEORIES FOR COMPLEXES BASED ON FLATS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-02
    LI LIANG

    In this paper, we introduce and study the Gorenstein relative homology theory for unbounded complexes of modules over arbitrary associative rings, which is defined using special Gorenstein flat precovers. We compare the Gorenstein relative homology to the Tate/unbounded homology and get some results that improve the known ones.

    更新日期:2019-12-02
  • HOW A NONASSOCIATIVE ALGEBRA REFLECTS THE PROPERTIES OF A SKEW POLYNOMIAL
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-11-26
    C. BROWN; S. PUMPLÜN

    Let D be a unital associative division ring and D[t, σ, δ] be a skew polynomial ring, where σ is an endomorphism of D and δ a left σ-derivation. For each f ϵ D[t, σ, δ] of degree m > 1 with a unit as leading coefficient, there exists a unital nonassociative algebra whose behaviour reflects the properties of f. These algebras yield canonical examples of right division algebras when f is irreducible

    更新日期:2019-11-26
  • OPERADIC APPROACH TO COHOMOLOGY OF ASSOCIATIVE TRIPLE AND N-TUPLE SYSTEMS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-11-14
    FATEMEH BAGHERZADEH; MURRAY BREMNER

    The cup product in the cohomology of algebras over quadratic operads has been studied in the general setting of Koszul duality for operads. We study the cup product on the cohomology of n-ary totally associative algebras with an operation of even (homological) degree. This cup product endows the cohomology with the structure of an n-ary partially associative algebra with an operation of even or odd

    更新日期:2019-11-14
  • (t, ℓ)-STABILITY AND COHERENT SYSTEMS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-09
    L. BRAMBILA-PAZ; O. MATA-GUTIÉRREZ

    Let X be a non-singular irreducible complex projective curve of genus g ≥ 2. The concept of stability of coherent systems over X depends on a positive real parameter α, given then a (finite) family of moduli spaces of coherent systems. We use (t, ℓ)-stability to prove the existence of coherent systems over X that are α-stable for all allowed α > 0.

    更新日期:2019-10-09
  • ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-07
    FLORIAN BOUYER

    In [5], Eklund showed that a general (ℤ/2ℤ)4 -invariant quartic K3 surface contains at least 320 conics. In this paper, we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space of (ℤ/2ℤ)4-invariant quartic K3 surface with a certain marked conic has 10 irreducible components.

    更新日期:2019-10-07
  • OPEN BOOKS FOR CLOSED NON-ORIENTABLE 3–MANIFOLDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-07
    ABHIJEET GHANWAT; SUHAS PANDIT; A SELVAKUMAR

    In this note, we give a new proof of the existence of an open book decomposition for a closed non-orientable 3–manifold. This open book decomposition is analogous to a planar open book decomposition for a closed orientable 3–manifold. More precisely, in this note, we give an open book decomposition of a given closed non-orientable 3–manifold with the pages punctured Möbius bands. We also give an algorithm

    更新日期:2019-10-07
  • DIVISION SUDOKUS: INVARIANTS, ENUMERATION, AND MULTIPLE PARTITIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-02
    ALEŠ DRÁPAL; PETR VOJTĚCHOVSKÝ

    A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time. We use nearfields and affine geometry to construct division sudokus of prime power rank that are rich

    更新日期:2019-10-02
  • POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-02
    DAVID KYED; HENRIK DENSING PETERSEN

    We introduce a refined version of group cohomology and relate it to the space of polynomials on the group in question. We show that the polynomial cohomology with trivial coefficients admits a description in terms of ordinary cohomology with polynomial coefficients, and that the degree one polynomial cohomology with trivial coefficients admits a description directly in terms of polynomials. Lastly

    更新日期:2019-10-02
  • QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-09-30
    QILIAN ZHENG; JIAQUN WEI

    The notion of mutation pairs of subcategories in an n-abelian category is defined in this paper. Let ${\cal D} \subseteq {\cal Z}$ be subcategories of an n-abelian category ${\cal A}$ . Then the quotient category ${\cal Z}/{\cal D}$ carries naturally an (n + 2) -angulated structure whenever $ ({\cal Z},{\cal Z}) $ forms a ${\cal D} \subseteq {\cal Z}$ -mutation pair and ${\cal Z}$ is extension-closed

    更新日期:2019-09-30
  • QUANTUM INCREASING SEQUENCES GENERATE QUANTUM PERMUTATION GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-09-27
    PAWEŁ JÓZIAK

    We answer a question of Skalski and Sołan (2016) about inner faithfulness of the Curran’s map of extending a quantum increasing sequence to a quantum permutation. Roughly speaking, we find a inductive setting in which the inner faithfulness of Curran’s map can be boiled down to inner faithfulness of similar map for smaller algebras and then rely on inductive generation result for quantum permutation

    更新日期:2019-09-27
  • BANACH ALGEBRAS OF VECTOR-VALUED FUNCTIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-09-06
    AZADEH NIKOU; ANTHONY G. O’FARRELL

    We correct an error in our paper published in volume 56 of this journal.

    更新日期:2019-09-06
  • COALTERNATIVE COALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-08-20
    HELENA ALBUQUERQUE; ELISABETE BARREIRO; JOSÉ M. SÁNCHEZ; CARLOS SONEIRA CALVO

    In this paper, we define a Cayley–Dickson process for k-coalgebras proving some results that describe the properties of the final coalgebra, knowing the properties of the initial one. Namely, after applying the Cayley–Dickson process for k-coalgebras to a coassociative coalgebra, we obtain a coalternative one. Moreover, the first coalgebra is cocommutative if and only if the final coalgebra is coassociative

    更新日期:2019-08-20
  • BIFURCATION PROPERTIES FOR A CLASS OF CHOQUARD EQUATION IN WHOLE ℝ3 - ERRATUM
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-08-14
    CLAUDIANOR O. ALVES; ROMILDO N. DE LIMA; ALÂNNIO B. NÓBREGA

    This paper concerns the study of some bifurcation properties for the following class of Choquard-type equations: (P) $$\left\{ {\begin{array}{*{20}{l}} { - \Delta u = \lambda f(x)\left[ {u + \left( {{I_\alpha }*f( \cdot )H(u)} \right)h(u)} \right],{\rm{ in }} \ {{\mathbb{R}}^3},}\\ {{{\lim }_{|x| \to \infty }}u(x) = 0,\quad u(x) > 0,\quad x \in {{\mathbb{R}}^3},\quad u \in {D^{1,2}}({{\mathbb{R}}^3})

    更新日期:2019-08-14
  • THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V2)
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-07-29
    VOLODYMYR V. BAVULA; TAO LU

    Let 𝔟 be the Borel subalgebra of the Lie algebra 𝔰𝔩2 and V2 be the simple two-dimensional 𝔰𝔩2-module. For the universal enveloping algebra $\[{\cal A}: = U(\gb \ltimes {V_2})\]$ of the semi-direct product 𝔟⋉V2 of Lie algebras, the prime, primitive and maximal spectra are classified. Please approve edit to the sentence “The sets of completely prime…”.The sets of completely prime ideals of $\[{\cal

    更新日期:2019-07-29
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