• Glasg. Math. J. (IF 0.548) Pub Date : 2021-01-14
DREW HEARD

Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson

更新日期：2021-01-14
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-12-18
DILETTA MARTINELLI

We prove that the number of MMP-series of a smooth projective threefold of positive Kodaira dimension and of Picard number equal to three is at most two.

更新日期：2020-12-18
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-12-09
MATTHEW PRESSLAND; JULIA SAUTER

We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting properties, for example, that their endomorphism algebras always have global dimension less than or equal to that of the original algebra. We characterise minimal d-Auslander–Gorenstein

更新日期：2020-12-18
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-12-01
MOTOKO KATO; SHIN-ICHI OGUNI

It is conjectured that the central quotient of any irreducible Artin–Tits group is either virtually cyclic or acylindrically hyperbolic. We prove this conjecture for Artin–Tits groups that are known to be CAT(0) groups by a result of Brady and McCammond, that is, Artin–Tits groups associated with graphs having no 3-cycles and Artin–Tits groups of almost large type associated with graphs admitting appropriate

更新日期：2020-12-18
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-12-01
NICOLÁS ANDRUSKIEWITSCH; DIRCEU BAGIO; SARADIA DELLA FLORA; DAIANA FLÔRES

We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are

更新日期：2020-12-18
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-11-24
DAISUKE KISHIMOTO; AKIHIRO OHSITA; MASAHIRO TAKEDA

We determine the (non-)triviality of Samelson products of inclusions of factors of the mod p decomposition of $G_{(p)}$ for $(G,p)=(E_7,5),(E_7,7),(E_8,7)$ . This completes the determination of the (non-)triviality of those Samelson products in p-localized exceptional Lie groups when G has p-torsion-free homology.

更新日期：2020-11-25
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-11-24
FILIP MISEV; GILBERTO SPANO

We show that there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery to an L-space, despite resembling algebraic knots and L-space knots in general: they are algebraically concordant to the torus knot T(2, 2g + 1) of the same genus and they are fibred and strongly quasipositive.

更新日期：2020-11-25
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-11-04
LUIS JORGE SÁNCHEZ SALDAÑA

We say a group G satisfies properties (M) and (NM) if every nontrivial finite subgroup of G is contained in a unique maximal finite subgroup, and every nontrivial finite maximal subgroup is self-normalizing. We prove that the Bredon cohomological dimension and the virtual cohomological dimension coincide for groups that admit a cocompact model for EG and satisfy properties (M) and (NM). Among the examples

更新日期：2020-11-04
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-11-03
JUNLING ZHENG; ZHAOYONG HUANG

Let Λ be an artin algebra and $0=I_{0}\subseteq I_{1} \subseteq I_{2}\subseteq\cdots \subseteq I_{n}$ a chain of ideals of Λ such that $(I_{i+1}/I_{i})\rad(\Lambda/I_{i})=0$ for any $0\leq i\leq n-1$ and $\Lambda/I_{n}$ is semisimple. If either none or the direct sum of exactly two consecutive ideals has infinite projective dimension, then the finitistic dimension conjecture holds for Λ. As a consequence

更新日期：2020-11-03
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-10-13

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-23

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 $\Phi(n)=\sum_{d|n} \frac{\log d}{d}$ . We extend this result to the function $\Psi(n)= \sum_{d|n} \frac{(\log d )(\log\log d)}{d}$ and some other functions. We show that $\limsup_{n\to \infty}\, \frac{\Psi(n)}{(\log\log n)^2(\log\log\log n)}\,=\, e^\gamma$ . The proof requires

更新日期：2020-05-13
• 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
• 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
• 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
• 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
• 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
• 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
• 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} where $q(x)$ is real-valued and integrable on [0, $\pi$ ]. Let $\{\lambda_n\}_{n\in \mathbb{Z}\setminus 更新日期：2020-04-07 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-06 R. DIÓGENES; E. RIBEIRO; E. RUFINO In this note, we prove that a four-dimensional compact oriented half-conformally flat Riemannian manifold M4 is topologically$\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]$In addition, we use the notion of biorthogonal (sectional) curvature to obtain a pinching condition which guarantees 更新日期：2020-04-06 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-16 ULRICH KRÄHMER; LUCIA ROTHERAY Incidence coalgebras of categories in the sense of Joni and Rota are studied, specifically cases where a monoidal product on the category turns these into (weak) bialgebras. The overlap with the theory of combinatorial Hopf algebras and that of Hopf quivers is discussed, and examples including trees, skew shapes, Milner’s bigraphs and crossed modules are considered. 更新日期：2020-03-16 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-12 SHENGBIN YU; JIANQING CHEN In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*} where 0 < γ < 1, λ > 0 and 0 < s ≤ t < 1 with 4s + 2t > 3 更新日期：2020-03-12 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-12 BOUALEM BENSEBAA; ABBAS MOVAHHEDI; ALAIN SALINIER It is proven that, for a wide range of integers s (2 < s < p − 2), the existence of a single wildly ramified odd prime l ≠ p leads to either the alternating group or the full symmetric group as Galois group of any irreducible trinomial Xp + aXs + b of prime degree p. 更新日期：2020-03-12 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-27 BIN HU; JIANHONG HUANG; ALEXANDER N. SKIBA Let G be a finite group and σ = {σi| i ∈ I} some partition of the set of all primes$\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}}$to denote the σ-nilpotent residual of G, that is, the intersection of all normal subgroups 更新日期：2020-02-27 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-26 DIKRAN DIKRANJAN; ANNA GIORDANO BRUNO; FRANCESCO G. RUSSO We study the locally compact abelian groups in the class${\mathfrak E_{ \lt \infty }}$, that is, having only continuous endomorphisms of finite topological entropy, and in its subclass$\mathfrak E_0$, that is, having all continuous endomorphisms with vanishing topological entropy. We discuss the reduction of the problem to the case of periodic locally compact abelian groups, and then to locally 更新日期：2020-02-26 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-19 MARINA AVITABILE; SANDRO MATTAREI We introduce a generalization${\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)$was previously investigated by the authors as the inverse, in an appropriate sense, of a parametrized generalization 更新日期：2020-02-19 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-03 DUNCAN MCCOY For p ≥ 1, one can define a generalisation of the unknotting number tup called the pth untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tup–1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large 更新日期：2020-02-03 • Glasg. Math. J. (IF 0.548) Pub Date : 2020-01-10 OLGUR CELIKBAS; RYO TAKAHASHI We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid and strongly rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion condition of a long-standing conjecture of Huneke and Wiegand. 更新日期：2020-01-10 • Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-20 ELOISA DETOMI; GURAM DONADZE; MARTA MORIGI; PAVEL SHUMYATSKY Let γn = [x1,…,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that$|{g^{{X_n}}}| \le m$for each g ∈ G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite. 更新日期：2019-12-20 • Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-12 LEONID CHAICHENETS; NIKOLAOS PATTAKOS We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces${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
• 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
• 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
• Glasg. Math. J. (IF 0.548) Pub Date : 2019-11-14

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
• 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
• 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
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