University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2
1
2014
08
01
Primal strong co-ideals in semirings
1
14
EN
S.
Ebrahimi Atani
University of Guilan
ebrahimi@guilan.ac.ir
S.
Dolati Pish Hesari
University of Guilan
saboura_dolati@yahoo.com
M.
Khoramdel
University of Guilan
mehdikhoramdel@gmail.com
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.
Prime strong co,Prime strong co-ideals,ideals,primal strong co-ideals,primal strong co,subtractive strong co-ideals,subtractive strong co
http://jart.guilan.ac.ir/article_56.html
http://jart.guilan.ac.ir/article_56_aa49e7fee2d91c7e37a8cc981dd8895e.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2
1
2014
08
01
Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications
15
25
EN
M.
Nasernejad
University of Payame Noor
nasernejad@phd.pnu.ac.ir
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 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.
Monomial ideals,associated prime ideals,trees,paths
http://jart.guilan.ac.ir/article_57.html
http://jart.guilan.ac.ir/article_57_45c5e51de657c1dc081bfad7d1fc6b80.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2
1
2014
08
01
The generalized total graph of modules respect to proper submodules over commutative rings.
27
42
EN
N. K.
Tohidi
Islamic Azad University
tohidi@iauo.ac.ir
F.
Esmaeili Khalil Saraei
University of Tehran
f.esmaeili.kh@ut.ac.ir
S. A.
Jalili
Islamic Azad University
jalili@iauo.ac.ir
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 $M(N,I)={min M : rmin N+IM for some rin R-I}$. The main purpose of this paper is to extend the definitions and properties given in [2] and [12] to a more general case.
Total graph,prime submodule,module
http://jart.guilan.ac.ir/article_58.html
http://jart.guilan.ac.ir/article_58_08720c0a97470138baf6f3d0ccee4594.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2
1
2014
08
01
Some results on Noetherian semigroup
43
53
EN
A. A.
Estaji
Hakim Sabzevari University
aaestaji@hsu.ac.ir
A. As.
Estaji
Hakim Sabzevari University
a_aestaji@hsu.ac.ir
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.
Prime ideal,Weakly Noetherian,Krull intersection theorem,prime ideal,Noetherian space
http://jart.guilan.ac.ir/article_59.html
http://jart.guilan.ac.ir/article_59_da9ae2a31636f14c6a2ba8347a7ccd93.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2
1
2014
08
01
Cubic symmetric graphs of orders $36p$ and $36p^{2}$
55
63
EN
M.
Alaeiyan
Iran University of Science and Technology
alaeiyan@iust.ac.ir
L.
Pourmokhtar
Iran University of Science and Technology
laleh_pourmokhtar@iust.ac.ir
M. K.
Hosseinpoor
Iran University of Science and Technology
mhossinipoor@iust.ac.ir
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.
Symmetric graphs,$s$-regular graphs
http://jart.guilan.ac.ir/article_60.html
http://jart.guilan.ac.ir/article_60_1860c42d3f206290b90bdc3557df68fd.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2
1
2014
08
01
A scheme over quasi-prime spectrum of modules
65
77
EN
A.
Abbasi
University of Guilan
aabbasi@guilan.ac.ir
D.
Hassanzadeh-Lelekaami
University of Guilan
dhmath@guilan.ac.ir
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 $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. 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 $M$.
Quasi,Quasi-prime submodule,prime submodule,quasi-primeful module,primeful module,quasi-prime-embedding module,developed Zariski topology,prime,embedding module
http://jart.guilan.ac.ir/article_61.html
http://jart.guilan.ac.ir/article_61_25bfba65b52ff4402f27084e6c3383e8.pdf