Shahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901MULTIPLICATION MODULES THAT ARE FINITELY GENERATED15176110.22044/jas.2019.8699.1421ENY. TolooeiDepartment of Mathematics, Faculty of Science, Razi University, Kermanshah,
67149-67346, Iran.0000-0002-0680-6932Journal Article20190714Let $R$ 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.https://jas.shahroodut.ac.ir/article_1761_b43d2dbad078483b14ce4c8a0a2df8fc.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901CLASSICAL 2-ABSORBING SECONDARY SUBMODULES715176210.22044/jas.2019.7287.1359ENF. FarshadifarDepartment of Mathematics, Farhangian University, Tehran, Iran.0000-0001-7600-994XJournal Article20180720In 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<br />identity. We say that a non-zero submodule $N$ of an $R$-module $M$ is a<br />\emph{classical 2-absorbing secondary submodule} of $M$ if whenever $a, b \in R$, $K$ is a submodule of $M$ and $abN\subseteq K$,<br />then $aN \subseteq K$ or $bN \subseteq K$ or $ab \in \sqrt{Ann_R(N)}$.<br />This can be regarded as a dual notion of the 2-absorbing primary submodule.https://jas.shahroodut.ac.ir/article_1762_45c478c6d71b1cbd202a21bc668d31f3.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS1726176310.22044/jas.2019.8356.1409ENM. R. Ahmadi ZandDepartment of Mathematics, Yazd University, P.O. Box 89195 - 741, Yazd, Iran.S. RostamiDepartment of Mathematics, Yazd University, P.O. Box 89195 - 741, Yazd, Iran.Journal Article20190427Abstract. A topological group H is called ω -narrow if for every<br />neighbourhood V of it’s identity element there exists a countable<br />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<br />such that xe(x) = e(x)x = x and for every x ∈ G there exists<br />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,<br />then G is called a topological generalized group. If {e(x) | x ∈ G} is<br />countable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrow<br />topological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topological<br />generalized groups are introduced and studiedhttps://jas.shahroodut.ac.ir/article_1763_7eca9f8c7119e52f92adbafaae64e02c.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS2737176410.22044/jas.2019.8295.1403ENR. KhosraviDepartment of Mathematics, Faculty of Sciences, Fasa University, P.O. Box: 74617-
81189, Fasa, Iran.M. RoueentanLamerd Higher Education Center, Lamerd, Iran.Journal Article20190413In 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.https://jas.shahroodut.ac.ir/article_1764_19902decb3c6a41c0cbf3f4368d348d7.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901ADMITTING CENTER MAPS ON MULTIPLICATIVE METRIC SPACE3951176510.22044/jas.2019.8055.1395ENM. H. LABBAF Ghasemi ZavarehDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.N. EftekhariDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.A. Bayati EshkaftakiDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.Journal Article20190207In this work, we investigate admitting center map on multiplicative metric space <br />and establish some fixed point theorems for such maps. We modify the Banach contraction principle and <br />the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some<br />useful theorems. Our results on multiplicative metric space improve and modify <br />some fixed point theorems in the literature.https://jas.shahroodut.ac.ir/article_1765_4fc36a723966485490273767e227e46e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE5368176610.22044/jas.2019.8320.1407ENH. BijariDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-
91775, Mashhad, Iran.K. KhashyarmaneshDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-
91775, Mashhad, Iran.H. Fazaeli MoghimDepartment of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand,
Iran.Journal Article20190420Let $R$ 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.https://jas.shahroodut.ac.ir/article_1766_bb94c6f535b2d77ed688e10b285d39ea.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901$\varphi$-CONNES MODULE AMENABILITY OF DUAL BANACH ALGEBRAS6982176710.22044/jas.2019.8503.1415ENA. GhaffariDepartment of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan,
Iran.S. Javadi SyahkaleFaculty of Engineering- East Guilan, University of Guilan, P.O. Box 44891-63157,
Rudsar, Iran.E. TamimiDepartment of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan,
Iran.Journal Article20190529In this paper we define $\varphi$-Connes module amenability of<br />a dual Banach algebra $\mathcal{A}$ where $\varphi$ is a bounded $w_{k^*}$-module<br />homomorphism from $\mathcal{A}$ to $\mathcal{A}$. We are mainly<br />concerned with the study of $\varphi$-module normal<br />virtual diagonals. We show that if $S$ is a weakly cancellative<br />inverse semigroup with subsemigroup $E$ of idempotents, $\chi$<br />is a bounded $w_{k^*}$-module homomorphism from $l^1(S)$ to $l^1(S)$ and $l^1(S)$<br />as a Banach module over $l^1(E)$ is $\chi$-Connes module amenable, then it has a $\chi$-module normal virtual<br />diagonal. In the case $\chi=id$, the converse holdshttps://jas.shahroodut.ac.ir/article_1767_75ba3bc94de55cd62417dc2836015b68.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G8393176810.22044/jas.2019.8314.1411ENGh. A. NasiriboroujeniDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad 91775, Iran.M. MirzavaziriDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad 91775, Iran.A. ErfanianDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20190506To a simple graph $G=(V,E)$, we correspond a simple graph $G_{\triangle,\square}$ whose vertex set is $\{\{x,y\}: x,y\in V\}$ and two vertices $\{x,y\},\{z,w\}\in G_{\triangle,\square}$ are adjacent if and only if $\{x,z\},\{x,w\},\{y,z\},\{y,w\}\in V\cup E$. 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 $G_{\triangle,\square}$.https://jas.shahroodut.ac.ir/article_1768_14cc474d2aefb94874aaa688ee9a3396.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X]95102176910.22044/jas.2019.8232.1401ENM. Seidali SamaniFaculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili,
P.O. Box 56199-11367, Ardabil, Iran.K. BahmanpourFaculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili,
P.O. Box 56199-11367, Ardabil, Iran.Journal Article20190407Let 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<br />cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp.<br />R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions<br />of local cohomology modules, and show that if the Lynch's conjecture, in [11], holds in<br />R[[X]], then it will holds in R.https://jas.shahroodut.ac.ir/article_1769_8358f552c2c0aeaab43aeb2d2290d1bf.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901A NEW CHARACTERIZATION OF SIMPLE GROUP G 2 (q) WHERE q ⩽ 11103111177010.22044/jas.2019.7696.1377ENM. BibakDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
3697, Tehran, Iran.Gh.R. RezaeezadehFaculty of Mathematical Sciences, Department of Pure Mathematics, University of
Shahrekord, P.O. Box 88186-34141, Shahrekord, Iran.0000-0002-0442-7269E. EsmaeilzadehDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
3697, Tehran, Iran.Journal Article20181116In this paper, we prove that every finite group $ G $ with the same order and largest element order as <br />$G_{2}(q)$, where $ q\leq 11 $ is necessarily isomorphic to the group $G_{2}(q)$.<br /><br />https://jas.shahroodut.ac.ir/article_1770_b640633c69aa4e00df345f85977f9251.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901A GENERALIZATION OF PRIME HYPERIDEALS113127177110.22044/jas.2019.8491.1412ENM. AnbarloeiDepartment of Mathematics, Faculty of Sciences, Imam Khomeini International
University, Qazvin, Iran.Journal Article20190525Let $R$ be a multiplicative hyperring. In this paper, we introduce and study the concept of n-absorbing hyperideal which is a generalization<br />of prime hyperideal. A proper hyperideal $I$ of $R$ is called an $n$-absorbing hyperideal of $R$ if whenever $\alpha_1o...o\alpha_{n+1} \subseteq I$ for $\alpha_1,...,\alpha_{n+1} \in R$, then there are $n$ of the $\alpha_i^,$s whose product is in $I$.https://jas.shahroodut.ac.ir/article_1771_d633f0db42fabb1c3bdf59b5d151e0a9.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901WOVEN FRAMES IN TENSOR PRODUCT OF HILBERT SPACES129140177210.22044/jas.2020.8890.1432ENS. Afshar JahanshahiDepartment of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar
Abbas, Iran.A. AhmadiDepartment of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar
Abbas, Iran.Journal Article20190906The tensor product is the fundemental ingredient for extending one-dimensional techniques of filtering and compression in signal preprocessing to higher dimensions. Woven frames play <br />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.https://jas.shahroodut.ac.ir/article_1772_e2b63dee96c10ca9a5820a8f6b7962cd.pdf