@article { author = {Farshadifar, F.}, title = {A generalization of pure submodules}, journal = {Journal of Algebra and Related Topics}, volume = {8}, number = {2}, pages = {1-8}, year = {2020}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2020.17279.1215}, abstract = {‎Let $R$ be a commutative ring with identity‎, ‎$S$ a multiplicatively closed subset of $R$‎, ‎and $M$ be an $R$-module‎. ‎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. ‎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.}, keywords = {Pure submodule‎,‎$S$-pure submodule‎,‎fully $S$-pure module}, url = {https://jart.guilan.ac.ir/article_4273.html}, eprint = {https://jart.guilan.ac.ir/article_4273_4b19a029613bb0a34b66dbc38bb6321c.pdf} } @article { author = {Ali, A. and Kumar, K.}, title = {Traces of permuting n-additive mappings in *-prime rings}, journal = {Journal of Algebra and Related Topics}, volume = {8}, number = {2}, pages = {9-21}, year = {2020}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2020.16288.1200}, abstract = {In 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 $\digamma: \underbrace{\Re\times \Re\times....\times \Re}_{n-times}\longrightarrow \Re$,$~\mbox{for all}~ x,y\in U$.}, keywords = {Prime rings,*-prime rings,*-Lie ideals,Trace of n-additive maps}, url = {https://jart.guilan.ac.ir/article_4274.html}, eprint = {https://jart.guilan.ac.ir/article_4274_9cec96569d82a11c9b42664966f8383f.pdf} } @article { author = {Louzari, M. and Ben Yakoub, L.}, title = {On $(\sigma,\delta)$-skew McCoy modules}, journal = {Journal of Algebra and Related Topics}, volume = {8}, number = {2}, pages = {23-37}, year = {2020}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2020.11937.1132}, abstract = {Let $(\sigma,\delta)$ 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.}, keywords = {McCoy module,skew McCoy module,semicommutative module,Armendariz module,reduced module}, url = {https://jart.guilan.ac.ir/article_4340.html}, eprint = {https://jart.guilan.ac.ir/article_4340_0d667fe68d704915ddc269242b0613f5.pdf} } @article { author = {Das, A. and Saha, M.}, title = {Determining Number of Some Families of Cubic Graphs}, journal = {Journal of Algebra and Related Topics}, volume = {8}, number = {2}, pages = {39-55}, year = {2020}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2020.16856.1209}, abstract = {The 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.}, keywords = {Automorphism groups,fixing number,cubic graphs}, url = {https://jart.guilan.ac.ir/article_4395.html}, eprint = {https://jart.guilan.ac.ir/article_4395_e661752d8724199cb817454ce3fc737d.pdf} } @article { author = {Bouchiba, S. and Arssi, Y.}, title = {On Property (A) of rings and modules over an ideal}, journal = {Journal of Algebra and Related Topics}, volume = {8}, number = {2}, pages = {57-74}, year = {2020}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2020.16259.1197}, abstract = {This 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.}, keywords = {Amalgamated duplication,A-ring,zero divisor}, url = {https://jart.guilan.ac.ir/article_4421.html}, eprint = {https://jart.guilan.ac.ir/article_4421_33a8988d0fbb3d0d2247a464dd3299ee.pdf} } @article { author = {Rakhsh Khorshid, N. and Ostadhadi-Dehkordi, S.}, title = {Relations between G-sets and their associate G^{\hat}-sets}, journal = {Journal of Algebra and Related Topics}, volume = {8}, number = {2}, pages = {75-91}, year = {2020}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2020.17806.1232}, abstract = {In this paper, we define and consider $G$-set on$\Gamma$-semihypergroups and we obtain relations between $G$-setsand their associate $\widehat{G}$-sets where $G$ is a$\Gamma$-semihypergroup and $\widehat{G}$ is an associatedsemihypergroup. Finally, we obtain the relation between direct limit of $\widehat{G}$-sets from the direct limit defined on $G$-sets.}, keywords = {Gamma-semihypergroup,G-set,G^{hat}-set,direct limit}, url = {https://jart.guilan.ac.ir/article_4422.html}, eprint = {https://jart.guilan.ac.ir/article_4422_2ba69b51a111a29742107433b92aaab6.pdf} }