Primal strong co-ideals in semirings
S.
Ebrahimi Atani
University of Guilan
author
S.
Dolati Pish Hesari
University of Guilan
author
M.
Khoramdel
University of Guilan
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
1
no.
2014
1
14
http://jart.guilan.ac.ir/article_56_aa49e7fee2d91c7e37a8cc981dd8895e.pdf
Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications
M.
Nasernejad
University of Payame Noor
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
1
no.
2014
15
25
http://jart.guilan.ac.ir/article_57_45c5e51de657c1dc081bfad7d1fc6b80.pdf
The generalized total graph of modules respect to proper submodules over commutative rings.
N. K.
Tohidi
Islamic Azad University
author
F.
Esmaeili Khalil Saraei
University of Tehran
author
S. A.
Jalili
Islamic Azad University
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
1
no.
2014
27
42
http://jart.guilan.ac.ir/article_58_08720c0a97470138baf6f3d0ccee4594.pdf
Some results on Noetherian semigroup
A. A.
Estaji
Hakim Sabzevari University
author
A. As.
Estaji
Hakim Sabzevari University
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
1
no.
2014
43
53
http://jart.guilan.ac.ir/article_59_da9ae2a31636f14c6a2ba8347a7ccd93.pdf
Cubic symmetric graphs of orders $36p$ and $36p^{2}$
M.
Alaeiyan
Iran University of Science and Technology
author
L.
Pourmokhtar
Iran University of Science and Technology
author
M. K.
Hosseinpoor
Iran University of Science and Technology
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
1
no.
2014
55
63
http://jart.guilan.ac.ir/article_60_1860c42d3f206290b90bdc3557df68fd.pdf
A scheme over quasi-prime spectrum of modules
A.
Abbasi
University of Guilan
author
D.
Hassanzadeh-Lelekaami
University of Guilan
author
text
article
2014
eng
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 $M$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
1
no.
2014
65
77
http://jart.guilan.ac.ir/article_61_25bfba65b52ff4402f27084e6c3383e8.pdf