@Article{EbrahimiAtani2014,
author="Ebrahimi Atani, S.
and Dolati Pish Hesari, S.
and Khoramdel, M.",
title="Primal strong co-ideals in semirings",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="1",
pages="1-14",
abstract="In this paper, we introduce the notion of primal strong co-ideals and give some results involving them. It is shown thatsubtractive 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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_56.html"
}
@Article{Nasernejad2014,
author="Nasernejad, M.",
title="Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="1",
pages="15-25",
abstract="Let $R$ 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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_57.html"
}
@Article{Tohidi2014,
author="Tohidi, N. K.
and Esmaeili Khalil Saraei, F.
and Jalili, S. A.",
title="The generalized total graph of modules respect to proper submodules over commutative rings.",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="1",
pages="27-42",
abstract="Let $M$ 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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_58.html"
}
@Article{Estaji2014,
author="Estaji, A. A.
and Estaji, A. As.",
title="Some results on Noetherian semigroup",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="1",
pages="43-53",
abstract="In 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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_59.html"
}
@Article{Alaeiyan2014,
author="Alaeiyan, M.
and Pourmokhtar, L.
and Hosseinpoor, M. K.",
title="Cubic symmetric graphs of orders $36p$ and $36p^{2}$",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="1",
pages="55-63",
abstract="A graph is \textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we classifyall 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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_60.html"
}
@Article{Abbasi2014,
author="Abbasi, A.
and Hassanzadeh-Lelekaami, D.",
title="A scheme over quasi-prime spectrum of modules",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="1",
pages="65-77",
abstract="The 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 $M$.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_61.html"
}