2014
2
1
1
77
Primal strong coideals in semirings
2
2
In this paper, we introduce the notion of primal strong coideals and give some results involving them. It is shown thatsubtractive strong coideals are intersection of all primal strong coideals that contain them. Also we prove that the representation of strong coideals as reduced intersections of primal strong coideals is unique.
1

1
14


S.
Ebrahimi Atani
University of Guilan
University of Guilan
Iran
ebrahimi@guilan.ac.ir


S.
Dolati Pish Hesari
University of Guilan
University of Guilan
Iran
saboura_dolati@yahoo.com


M.
Khoramdel
University of Guilan
University of Guilan
Iran
mehdikhoramdel@gmail.com
Prime strong co
Prime strong coideals
ideals
primal strong coideals
primal strong co
subtractive strong coideals
subtractive strong co
Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications
2
2
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 $kgeq 1$, which $mathrm{Ass}_R(R/I)$ denotes the set of associated prime ideals of $I$. In this paper, we introduce a class of squarefree 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 torsionfreeness of monomial ideals.
1

15
25


M.
Nasernejad
University of Payame Noor
University of Payame Noor
Iran
nasernejad@phd.pnu.ac.ir
Monomial ideals
associated prime ideals
trees
paths
The generalized total graph of modules respect to proper submodules over commutative rings.
2
2
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 $m,nin M$, the vertices $m$ and $n$ are adjacent if and only if $m+nin M(N,I)$, where $M(N,I)={min M : rmin N+IM for some rin RI}$. The main purpose of this paper is to extend the definitions and properties given in [2] and [12] to a more general case.
1

27
42


N. K.
Tohidi
Islamic Azad University
Islamic Azad University
Iran
tohidi@iauo.ac.ir


F.
Esmaeili Khalil Saraei
University of Tehran
University of Tehran
Iran
f.esmaeili.kh@ut.ac.ir


S. A.
Jalili
Islamic Azad University
Islamic Azad University
Iran
jalili@iauo.ac.ir
Total graph
prime submodule
module
Some results on Noetherian semigroup
2
2
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.
1

43
53


A. A.
Estaji
Hakim Sabzevari University
Hakim Sabzevari University
Iran
aaestaji@hsu.ac.ir


A. As.
Estaji
Hakim Sabzevari University
Hakim Sabzevari University
Iran
a_aestaji@hsu.ac.ir
prime ideal
Weakly Noetherian
Krull intersection theorem
prime ideal
Noetherian space
Cubic symmetric graphs of orders $36p$ and $36p^{2}$
2
2
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.
1

55
63


M.
Alaeiyan
Iran University of Science and Technology
Iran University of Science and Technology
Iran
alaeiyan@iust.ac.ir


L.
Pourmokhtar
Iran University of Science and Technology
Iran University of Science and Technology
Iran
laleh_pourmokhtar@iust.ac.ir


M. K.
Hosseinpoor
Iran University of Science and Technology
Iran University of Science and Technology
Iran
mhossinipoor@iust.ac.ir
Symmetric graphs
$s$regular graphs
A scheme over quasiprime spectrum of modules
2
2
The notions of quasiprime 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 $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. 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 $Mrightarrow N$, and also by ring homomorphism $Rrightarrow S$. Among other results, we show that $(X, mathcal{O}_X)$ is a scheme by putting some suitable conditions on $M$.
1

65
77


A.
Abbasi
University of Guilan
University of Guilan
Iran
aabbasi@guilan.ac.ir


D.
HassanzadehLelekaami
University of Guilan
University of Guilan
Iran
dhmath@guilan.ac.ir
Quasi
Quasiprime submodule
prime submodule
quasiprimeful module
primeful module
quasiprimeembedding module
developed Zariski topology
prime
embedding module