University of GuilanJournal of Algebra and Related Topics2345-39318220201201A generalization of pure submodules18427310.22124/jart.2020.17279.1215ENF.FarshadifarUniversity of Farhangian, Tehran, Iran.Journal Article20200731Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module.<br /> The goal of this work is to introduce the notion of $S$-pure submodules of $M$ as a generalization of pure submodules of $M$ and prove a number of results concerning of this class of modules.<br /> We say that a submodule $N$ of $M$ is \emph {$S$-pure} if there exists an $s \in S$ such that $s(N \cap IM) \subseteq IN$ for every ideal $I$ of $R$. Also, We say that $M$ is \emph{fully $S$-pure} if every submodule of $M$ is $S$-pure.https://jart.guilan.ac.ir/article_4273_4b19a029613bb0a34b66dbc38bb6321c.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39318220201201Traces of permuting n-additive mappings in *-prime rings921427410.22124/jart.2020.16288.1200ENA.AliDepartment of Mathematics
Aligarh Muslim University, Aligarh, India0000-0001-7602-0268K.KumarDepartment of Mathematics
Aligarh Muslim University, Aligarh, India11orcid.org1000000003-437-8775Journal Article20200418In this paper, we prove that a nonzero square closed $*$-Lie ideal $U$ of a $*$-prime ring $\Re$ of Char $\Re$ $\neq$ $(2^{n}-2)$ is central, if one of the following holds: $(i)\delta(x)\delta(y)\mp x\circ y\in Z(\Re),$ $(ii)[x,y]-\delta(xy)\delta(yx)\in Z(\Re),$ $(iii)\delta(x)\circ \delta(y)\mp [x,y]\in Z(\Re),$ $(iv)\delta(x)\circ \delta(y)\mp xy\in Z(\Re),$ $(v) \delta(x)\delta(y)\mp yx\in Z(\Re),$ where $\delta$ is the trace of $n$-additive map $\digamma: \underbrace{\Re\times \Re\times....\times \Re}_{n-times}\longrightarrow \Re$,$~\mbox{for all}~ x,y\in U$.https://jart.guilan.ac.ir/article_4274_9cec96569d82a11c9b42664966f8383f.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39318220201201On $(\sigma,\delta)$-skew McCoy modules2337434010.22124/jart.2020.11937.1132ENM.LouzariDepartment of mathematics, Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, Morocco.0000-0002-3122-2701L.Ben YakoubDepartment of
Mathematics, University Abdelmalek Essaadi, Tetouan, Morocco.Journal Article20181210Let $(\sigma,\delta)$ be a quasi derivation of a ring $R$ and $M_R$ a right $R$-module. In this paper, we introduce the notion of $(\sigma,\delta)$-skew McCoy modules which extends the notion of McCoy modules and $\sigma$-skew McCoy modules. This concept can be regarded also as a generalization of $(\sigma,\delta)$-skew Armendariz modules. We study some connections between reduced modules, semicommutative modules, $(\sigma,\delta)$-compatible modules and $(\sigma,\delta)$-skew McCoy modules. Furthermore, we will give some results showing that the property of being an $(\sigma,\delta)$-skew McCoy module transfers well from a module $M_R$ to its skew triangular matrix extensions and vice versa.https://jart.guilan.ac.ir/article_4340_0d667fe68d704915ddc269242b0613f5.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39318220201201Determining Number of Some Families of Cubic Graphs3955439510.22124/jart.2020.16856.1209ENA.DasDepartment of
Mathematics, Presidency University, Kolkata, India.M.SahaDepartment of
Mathematics, Presidency University, Kolkata, India.Journal Article20200617The determining number of a graph $G = (V,E)$ is the minimum cardinality of a set $S\subseteq V$ such that pointwise stabilizer of $S$ under the action of $Aut(G)$ is trivial. In this paper, we compute the determining number of some families of cubic graphs.https://jart.guilan.ac.ir/article_4395_e661752d8724199cb817454ce3fc737d.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39318220201201On Property (A) of rings and modules over an ideal5774442110.22124/jart.2020.16259.1197ENS.BouchibaDepartment of Mathematics, Faculty of Sciences, University Moulay Ismail, Meknes, MoroccoY.ArssiDepartment of Mathematics, Faculty of Sciences, University Moulay Ismail, Meknes, MoroccoJournal Article20200414This paper introduces and studies the notion of Property ($\mathcal A$) of a ring $R$ or an $R$-module $M$ along an ideal $I$ of $R$. For instance, any module $M$ over $R$ satisfying the Property ($\mathcal A$) do satisfy the Property ($\mathcal A$) along any ideal $I$ of $R$. We are also interested in ideals $I$ which are $\mathcal A$-module along themselves. In particular, we prove that if $I$ is contained in the nilradical of $R$, then any $R$-module is an $\mathcal A$-module along $I$ and, thus, $I$ is an $\mathcal A$-module along itself. Also, we present an example of a ring $R$ possessing an ideal $I$ which is an $\mathcal A$-module along itself while $I$ is not an $\mathcal A$-module. Moreover, we totally characterize rings $R$ satisfying the Property ($\mathcal A$) along an ideal $I$ in both cases where $I\subseteq \Z(R)$ and where $I\nsubseteq \Z(R)$. Finally, we investigate the behavior of the Property ($\mathcal A$) along an ideal with respect to direct products.https://jart.guilan.ac.ir/article_4421_33a8988d0fbb3d0d2247a464dd3299ee.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39318220201201Relations between G-sets and their associate G^{\hat}-sets7591442210.22124/jart.2020.17806.1232ENN.Rakhsh KhorshidDepartment of Mathematics, University of Hormozgan, Bandar Abbas, IranS.Ostadhadi-DehkordiDepartment of Mathematics, University of Hormozgan, Bandar Abbas, IranJournal Article20200927In this paper, we define and consider $G$-set on<br />$\Gamma$-semihypergroups and we obtain relations between $G$-sets<br />and their associate $\widehat{G}$-sets where $G$ is a<br />$\Gamma$-semihypergroup and $\widehat{G}$ is an associated<br />semihypergroup. Finally, we obtain the relation between direct limit of $\widehat{G}$-sets from the direct limit defined on<br /> $G$-sets.https://jart.guilan.ac.ir/article_4422_2ba69b51a111a29742107433b92aaab6.pdf