University of GuilanJournal of Algebra and Related Topics2345-39312120140601Primal strong co-ideals in semirings11456ENS.Ebrahimi AtaniUniversity of GuilanS.Dolati Pish HesariUniversity of GuilanM.KhoramdelUniversity of GuilanJournal Article20131215In this paper, we introduce the notion of primal strong co-ideals and give some results involving them. It is shown that<br />subtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. Also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.https://jart.guilan.ac.ir/article_56_aa49e7fee2d91c7e37a8cc981dd8895e.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312120140601Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications152557ENM.NasernejadUniversity of Payame NoorJournal Article20140107Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. We say that $I$ satisfies the persistence property if $\mathrm{Ass}_R(R/I^k)\subseteq \mathrm{Ass}_R(R/I^{k+1})$ for all positive integers $k\geq 1$, which $\mathrm{Ass}_R(R/I)$ denotes the set of associated prime ideals of $I$. In this paper, we introduce a class of square-free monomial ideals in the polynomial ring $R=K[x_1,\ldots,x_n]$ over field $K$ which are associated to unrooted trees such that if $G$ is a unrooted tree and $I_t(G)$ is the ideal generated by the paths of $G$ of length $t$, then $J_t(G):=I_t(G)^\vee$, where $I^\vee$ denotes the Alexander dual of $I$, satisfies the persistence property. We also present a class of graphs such that the path ideals generated by paths of length two satisfy the persistence property. We conclude this paper by giving a criterion for normally torsion-freeness of monomial ideals.https://jart.guilan.ac.ir/article_57_45c5e51de657c1dc081bfad7d1fc6b80.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312120140601The generalized total graph of modules respect to proper submodules over commutative rings.274258ENN. K.TohidiIslamic Azad UniversityF.Esmaeili Khalil SaraeiUniversity of TehranS. A.JaliliIslamic Azad UniversityJournal Article20130830Let $M$ be a module over a commutative ring $R$ and let $N$ be a proper submodule of $M$. The total graph of $M$ over $R$ with respect to $N$, denoted by $T(\Gamma_{N}(M))$, have been introduced and studied in [2]. In this paper, A generalization of the total graph $T(\Gamma_{N}(M))$, denoted by $T(\Gamma_{N,I}(M))$ is presented, where $I$ is an ideal of $R$. It is the graph with all elements of $M$ as vertices, and for distinct $m,n\in M$, the vertices $m$ and $n$ are adjacent if and only if $m+n\in M(N,I)$, where $M(N,I)=\{m\in M : rm\in N+IM \ for \ some \ \ r\in R-I\}$. The main purpose of this paper is to extend the definitions and properties given in [2] and [12] to a more general case.https://jart.guilan.ac.ir/article_58_08720c0a97470138baf6f3d0ccee4594.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312120140601Some results on Noetherian semigroup435359ENA. A.EstajiHakim Sabzevari UniversityA. As.EstajiHakim Sabzevari UniversityJournal Article20140212In this paper we study some results on Noetherian semigroups. We show that if $S_S$ is an strongly faithful $S$-act and $S$ is a duo weakly Noetherian, then we have the following.https://jart.guilan.ac.ir/article_59_da9ae2a31636f14c6a2ba8347a7ccd93.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312120140601Cubic symmetric graphs of orders $36p$ and $36p^{2}$556360ENM.AlaeiyanIran University of Science and TechnologyL.PourmokhtarIran University of Science and TechnologyM. K.HosseinpoorIran University of Science and TechnologyJournal Article20140406A graph is \textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we classify<br />all the connected cubic symmetric graphs of order $36p$ and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.https://jart.guilan.ac.ir/article_60_1860c42d3f206290b90bdc3557df68fd.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312120140601A scheme over quasi-prime spectrum of modules657761ENA.AbbasiUniversity of GuilanD.Hassanzadeh-LelekaamiUniversity of GuilanJournal Article20140125The notions of quasi-prime submodules and developed Zariski topology was introduced by the present authors in \cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:=\{Q\in q\Spec(M) \mid (Q:_R M)\in\Spec(R)\}$. It is proved that $(X, \mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $M\rightarrow N$, and also by ring homomorphism $R\rightarrow S$. Among other results, we show that $(X, \mathcal{O}_X)$ is a scheme by putting some suitable conditions on $M$.https://jart.guilan.ac.ir/article_61_25bfba65b52ff4402f27084e6c3383e8.pdf