ORIGINAL_ARTICLE
Primal strong co-ideals in semirings
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.
https://jart.guilan.ac.ir/article_56_aa49e7fee2d91c7e37a8cc981dd8895e.pdf
2014-06-01T11:23:20
2019-04-22T11:23:20
1
14
Prime strong co
Prime strong co-ideals
ideals
primal strong co-ideals
primal strong co
subtractive strong co-ideals
subtractive strong co
S.
Ebrahimi Atani
ebrahimi@guilan.ac.ir
true
1
University of Guilan
University of Guilan
University of Guilan
LEAD_AUTHOR
S.
Dolati Pish Hesari
saboura_dolati@yahoo.com
true
2
University of Guilan
University of Guilan
University of Guilan
AUTHOR
M.
Khoramdel
mehdikhoramdel@gmail.com
true
3
University of Guilan
University of Guilan
University of Guilan
AUTHOR
ORIGINAL_ARTICLE
Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications
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.
https://jart.guilan.ac.ir/article_57_45c5e51de657c1dc081bfad7d1fc6b80.pdf
2014-06-01T11:23:20
2019-04-22T11:23:20
15
25
Monomial ideals
associated prime ideals
trees
paths
M.
Nasernejad
nasernejad@phd.pnu.ac.ir
true
1
University of Payame Noor
University of Payame Noor
University of Payame Noor
LEAD_AUTHOR
ORIGINAL_ARTICLE
The generalized total graph of modules respect to proper submodules over commutative rings.
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.
https://jart.guilan.ac.ir/article_58_08720c0a97470138baf6f3d0ccee4594.pdf
2014-06-01T11:23:20
2019-04-22T11:23:20
27
42
Total graph
prime submodule
module
N. K.
Tohidi
tohidi@iauo.ac.ir
true
1
Islamic Azad University
Islamic Azad University
Islamic Azad University
LEAD_AUTHOR
F.
Esmaeili Khalil Saraei
f.esmaeili.kh@ut.ac.ir
true
2
University of Tehran
University of Tehran
University of Tehran
AUTHOR
S. A.
Jalili
jalili@iauo.ac.ir
true
3
Islamic Azad University
Islamic Azad University
Islamic Azad University
AUTHOR
ORIGINAL_ARTICLE
Some results on Noetherian semigroup
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.
https://jart.guilan.ac.ir/article_59_da9ae2a31636f14c6a2ba8347a7ccd93.pdf
2014-06-01T11:23:20
2019-04-22T11:23:20
43
53
prime ideal
Weakly Noetherian
Krull intersection theorem
prime ideal
Noetherian space
A. A.
Estaji
aaestaji@hsu.ac.ir
true
1
Hakim Sabzevari University
Hakim Sabzevari University
Hakim Sabzevari University
LEAD_AUTHOR
A. As.
Estaji
a_aestaji@hsu.ac.ir
true
2
Hakim Sabzevari University
Hakim Sabzevari University
Hakim Sabzevari University
AUTHOR
ORIGINAL_ARTICLE
Cubic symmetric graphs of orders $36p$ and $36p^{2}$
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.
https://jart.guilan.ac.ir/article_60_1860c42d3f206290b90bdc3557df68fd.pdf
2014-06-01T11:23:20
2019-04-22T11:23:20
55
63
Symmetric graphs
$s$-regular graphs
M.
Alaeiyan
alaeiyan@iust.ac.ir
true
1
Iran University of Science and Technology
Iran University of Science and Technology
Iran University of Science and Technology
LEAD_AUTHOR
L.
Pourmokhtar
laleh_pourmokhtar@iust.ac.ir
true
2
Iran University of Science and Technology
Iran University of Science and Technology
Iran University of Science and Technology
AUTHOR
M. K.
Hosseinpoor
mhossinipoor@iust.ac.ir
true
3
Iran University of Science and Technology
Iran University of Science and Technology
Iran University of Science and Technology
AUTHOR
ORIGINAL_ARTICLE
A scheme over quasi-prime spectrum of modules
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 $M$.
https://jart.guilan.ac.ir/article_61_25bfba65b52ff4402f27084e6c3383e8.pdf
2014-06-01T11:23:20
2019-04-22T11:23:20
65
77
Quasi
Quasi-prime submodule
prime submodule
quasi-primeful module
primeful module
quasi-prime-embedding module
developed Zariski topology
prime
embedding module
A.
Abbasi
aabbasi@guilan.ac.ir
true
1
University of Guilan
University of Guilan
University of Guilan
LEAD_AUTHOR
D.
Hassanzadeh-Lelekaami
dhmath@guilan.ac.ir
true
2
University of Guilan
University of Guilan
University of Guilan
AUTHOR