Journal of Algebraic SystemsJournal of Algebraic Systems
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Feed provided by Journal of Algebraic Systems. Click to visit.MULTIPLICATION MODULES THAT ARE FINITELY GENERATED
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Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a characterization of finitely generated multiplication modules.Mon, 31 Aug 2020 19:30:00 +0100CLASSICAL 2-ABSORBING SECONDARY SUBMODULES
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‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ if whenever $a‎, ‎b in R$‎, ‎$K$ is a submodule of $M$ and $abNsubseteq K$‎, ‎then $aN subseteq K$ or $bN subseteq K$ or $ab in sqrt{Ann_R(N)}$‎. ‎This can be regarded as a dual notion of the 2-absorbing primary submodule‎.Mon, 31 Aug 2020 19:30:00 +0100ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS
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Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also let G be a topological space and the operation and inversion mapping are continuous, then G is called a topological generalized group. If {e(x) | x ∈ G} is countable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrow topological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topological generalized groups are introduced and studiedMon, 31 Aug 2020 19:30:00 +0100A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS
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In this paper, we investigate po-purity using ﬁnitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly ﬁnitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right congruence on S. Finally, the relationships between regular injectivity and absolute po-purity are considered.Mon, 31 Aug 2020 19:30:00 +0100ADMITTING CENTER MAPS ON MULTIPLICATIVE METRIC SPACE
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‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎some fixed point theorems in the literature‎.Mon, 31 Aug 2020 19:30:00 +0100PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE
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‎‎Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎We define the primary spectrum of $M$‎, ‎denoted by $mathcal{PS}(M)$‎, ‎to be the set of all primary submodules $Q$ of $M$ such that $(operatorname{rad}Q:M)=sqrt{(Q:M)}$‎. ‎In this paper‎, ‎we topologize $mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $operatorname{Spec}(M)$ as a subspace topology‎. ‎We investigate compactness and irreducibility of this topological space and provide some conditions under which $mathcal{PS}(M)$ is a spectral space‎.Mon, 31 Aug 2020 19:30:00 +0100$\varphi$-CONNES MODULE AMENABILITY OF DUAL BANACH ALGEBRAS
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In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idempotents, $chi$ is a bounded $w_{k^*}$-module homomorphism from $l^1(S)$ to $l^1(S)$ and $l^1(S)$ as a Banach module over $l^1(E)$ is $chi$-Connes module amenable, then it has a $chi$-module normal virtual diagonal. In the case $chi=id$, the converse holdsMon, 31 Aug 2020 19:30:00 +0100THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G
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To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the connectedness of $G$ and $G_{triangle,square}$.Mon, 31 Aug 2020 19:30:00 +0100ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X]
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Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, in [11], holds in R[[X]], then it will holds in R.Mon, 31 Aug 2020 19:30:00 +0100A NEW CHARACTERIZATION OF SIMPLE GROUP G 2 (q) WHERE q ⩽ 11
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Let G be a finite group , in this paper using the order and largest element order of G we show that every ﬁnite group with the same order and largest element order as G 2 (q), where q 11 is necessarily isomorphic to the group G 2 (q)Mon, 31 Aug 2020 19:30:00 +0100A GENERALIZATION OF PRIME HYPERIDEALS
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‎‎Let $R$ be a multiplicative hyperring‎. In this paper‎, ‎we introduce and study the concept of n-absorbing hyperideal which is a generalization‎ ‎of prime hyperideal‎. ‎A proper hyperideal $I$ of $R$ is called an $n$-absorbing hyperideal of ‎$‎R‎$‎ if whenever $alpha_1o...oalpha_{n+1} subseteq I$ for $alpha_1,...,alpha_{n+1} in R$‎, ‎then there are $n$ of the $alpha_i^,$s whose product is in $I$‎.Mon, 31 Aug 2020 19:30:00 +0100WOVEN FRAMES IN TENSOR PRODUCT OF HILBERT SPACES
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‎‎The tensor product is the fundemental ingredient for extending one-dimensional techniques of filtering and compression in signal preprocessing to higher dimensions‎. ‎Woven frames play ‎ a crucial role in signal preprocessing and distributed data processing‎. Motivated by these facts, we have investigated the tensor product of woven frames and presented some of their properties. Besides, we have studied some effects of operators on woven frames in the tensor products of Hilbert spaces.Mon, 31 Aug 2020 19:30:00 +0100