The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between LDunford-Pettis, and Dunford-Pettis (relatively compact) sets in

The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let K be a unital commutative ring, not necessarily a field. Given a unital K-algebra S, where K is contained in the center of S, n ∈ ℕ, the goal of this paper is to study the question: when can a homomorphism φ: Mn(K) → Mn(S) be extended to an inner

A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval

Let α and β be automorphisms of a nilpotent p-group G of finite rank. Suppose that 〈(αβ(g))(βα(g))–: g ∈G〉 is a finite cyclic subgroup of G, then, exclusively, one of the following statements holds for G and Γ, where Γ is the group generated by α and β. (i) G is finite, then Γ is an extension of a p-group by an abelian group. (ii) G is infinite, then Γ is soluble and abelian-by-finite.

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. We say M has maximal depth if there is an associated prime p of M such that depth M = dim R/p. In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.

A ring R is called right P-injective if every homomorphism from a principal right ideal of R to RR can be extended to a homomorphism from RR to RR. Let R be a ring and G a group. Based on a result of Nicholson and Yousif, we prove that the group ring RG is right P-injective if and only if (a) R is right P-injective; (b) G is locally finite; and (c) for any finite subgroup H of G and any principal right

We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain. \(D_{n,m}^p(\mu ).\) The generalized Fock-Bargmann-Hartogs domain is defined by inequality \({e^{\mu z{^2}}}\sum\limits_{j = 1}^m {{\omega _j}{^{2p}}} 1,\) where (z, ω) ∈ ℂn × ℂn. In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic

Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and δ: I(R) → I(R) an expansion of ideals of R defined by I ↦ δ(I). We introduce the concept of (δ, 2)-primary ideals in commutative rings. A proper ideal I of R is called a (δ, 2)-primary ideal if whenever a, b ∈ R and ab ∈ I, then a2 ∈ I or b2 ∈ δ(I). Our purpose is to extend the concept of 2-ideals to (δ, 2)-primary

Let R be a commutative ring with identity. If a ring R is contained in an arbitrary union of rings, then R is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in R, then R contains one of them under various conditions.

In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure (φ, ξ, η, g) induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that

An eigenvalue of a real symmetric matrix is called main if there is an associated eigenvector not orthogonal to the all-1 vector j. Main eigenvalues are frequently considered in the framework of simple undirected graphs. In this study we generalize some results and then apply them to signed graphs.

We prove convergence results for ‘increasing’ sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.

We determine explicitly the structure of the torsion group over the maximal abelian extension of ℚ and over the maximal p-cyclotomic extensions of ℚ for the family of rational elliptic curves given by y2 = x3 + B, where B is an integer.

Let R be a commutative ring with unity. The notion of maximal non valuation domain in an integral domain is introduced and characterized. A proper subring R of an integral domain S is called a maximal non valuation domain in S if R is not a valuation subring of S, and for any ring T such that R ⊂ T ⊂ S, T is a valuation subring of S. For a local domain S, the equivalence of an integrally closed maximal

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we show that fermionic Novikov algebras equipped with invariant non-degenerate symmetric bilinear forms are Novikov algebras.

Let H4 and H8 be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through H8 and H4 (equivalently, any bicrossed product between the Hopf algebras H8 and H4) must be isomorphic to one of the following four Hopf algebras: H8 ⊗ H4,H32,1,H32,2,H32,3. The set of all matched pairs (H4,H4, ⊳, ⊲) is explicitly described, and then the associated

Let ε be an algebraic unit of the degree n ⩾ 3. Assume that the extension ℚ(ε)/ℚ is Galois. We would like to determine when the order ℤ[ε] of ℚ(ε) is Gal(ℚ(ε)/ℚ)-invariant, i.e. when the n complex conjugates ε1, …, εn of ε are in ℤ[ε], which amounts to asking that ℤ[ε1, …, εn] = ℤ[ε], i.e., that these two orders of ℚ(ε) have the same discriminant. This problem has been solved only for n = 3 by using

It is known that a set H of positive integers is a Poincaré set (also called intersective set, see I. Ruzsa (1982)) if and only if dimH(XH) = 0, where [{X_H}: = left{ {x = ♪m⌜mits_{n = 1}^infty {↡ac{{{x_n}}}{{{2^n}}}:{x_n} in left{ {0,1} ⌝ght},{x_n}{x_{n + h}} = 0,for,all,n ε 1,,h in H} } ⌝ght}] and dimH denotes the Hausdorff dimension (see C. Bishop, Y. Peres (2017), Theorem 2.5.5). In this paper

This paper identifies a class of complex symmetric weighted composition operators on H2(D) that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight

We establish the boundedness for the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belonging to both Lipschitz space and central BMO space. By these, we generalize and strengthen some previously known results.

In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin

In this paper, we find all Pell and Pell-Lucas numbers written in the form −2a − 3b + 5c, in nonnegative integers a, b, c, with 0 ⩽ max{a, b} ⩽ c.

Suppose that G is a finite group and H is a subgroup of G. Subgroup H is said to be weakly \({\cal M}\)-supplemented in G if there exists a subgroup B of G such that (1) G = HB, and (2) if H1/HG is a maximal subgroup of H/HG, then H1B = BH1 < G, where HG is the largest normal subgroup of G contained in H. We fix in every noncyclic Sylow subgroup P of G a subgroup D satisfying 1 < ∣D∣ < ∣P∣ and study

We show that n-dimensional (n ⩾ 2) complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure n-space (i.e. the Euclidean metric n-space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted

We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.

Let \({\rm{Let}}\;f = \sum\limits_{n = 1}^\infty {a(n){q^n} \in {S_{k + 1/2}}(N,{\chi _0})} \) be a nonzero cuspidal Hecke eigenform of weight \(k + {1 \over 2}\) and the trivial nebentypus χ0, where the Fourier coefficients a(n) are real. Bruinier and Kohnen conjectured that the signs of a(n) are equidistributed. This conjecture was proved to be true by Inam, Wiese and Arias-de-Reyna for the subfamilies

Given a graph G, if there is no nonisomorphic graph H such that G and H have the same signless Laplacian spectra, then we say that G is Q-DS. In this paper we show that every fan graph Fn is Q-DS, where Fn = K1 ∨ Pn−1 and n ⩾ 3.

A ring extension R ⊆ S is said to be strongly affine if each R-subalgebra of S is a finite-type R-algebra. In this paper, several characterizations of strongly affine extensions are given. For instance, we establish that if R is a quasi-local ring of finite dimension, then R ⊆ S is integrally closed and strongly affine if and only if R ⊆ S is a Prüfer extension (i.e. (R, S) is a normal pair). As a

We determine the distribution over square-free integers n of the pair \(({\dim _{{\mathbb{F}_2}}}{\rm{Se}}{{\rm{l}}^\Phi}(E_n/\mathbb{Q})\), \({\dim _{{\mathbb{F}_2}}}{\rm{Se}}{{\rm{l}}^{\widehat\Phi}}(E_n^\prime /\mathbb{Q}))\), where En is a curve in the congruent number curve family, E′n: y2 = x3 + 4n2x is the image of isogeny Φ: En → E′n, Φ(x, y) = (y2/x2, y(n2 − x2)/x2), and \(\widehat\Phi \)

We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of ℝn+1 (n ⩾ 2) is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces are shown. Besides, under different

for a graph G = (V, E), a double Roman dominating function is a function f: V → {0, 1, 2, 3} having the property that if f (v) = 0, then the vertex v must have at least two neighbors assigned 2 under f or one neighbor with f (w) = 3, and if f (v) = 1, then the vertex v must have at least one neighbor with f (w) ⩾ 2. The weight of a double Roman dominating function f is the sum \(f(V) = \sum\nolimits_{v

We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the n-replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.

We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory

Let G be a group. A subgroup H of G is called a TI-subgroup if H ⋂ Hg = 1 or H for every g ∈ G and H is called a QTI-subgroup if CG(x) ⩽ NG(H) for any 1 ≠ x ∈ H. In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.

We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups GA(2) = GL(2, ℝ) ⋉ ℝ2 and GA(3) = GL(3, ℝ) ⋉ ℝ3, respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and

A proper vertex coloring of a graph G is acyclic if there is no bicolored cycle in G. In other words, each cycle of G must be colored with at least three colors. Given a list assignment L = {L(v): v ∈ V}, if there exists an acyclic coloring π of G such that π(v) ∈ L(v) for all v ∈ V, then we say that G is acyclically L-colorable. If G is acyclically L-colorable for any list assignment L with ∣L(v)∣

Let (R, \(\mathfrak{m}\)) be a commutative Noetherian local ring, \(\mathfrak{a}\) be an ideal of R and M a finitely generated R-module such that \(\mathfrak{a}M \ne M\) and cd(\(\mathfrak{a}\), M) — grade(\(\mathfrak{a}\), M) ⩽ 1, where cd(\(\mathfrak{a}\), M) is the cohomological dimension of M with respect to \(\mathfrak{a}\) and grade(\(\mathfrak{a}\), M) is the M-grade of \(\mathfrak{a}\). Let

We will show the blow-up of smooth solutions to the Cauchy problems for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing and compressible bipolar isentropic Navier-Stokes-Poisson equations in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between the physical quantities and establishing some differential