http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS
Atani, Shahabaddin Ebrahimi,Hesari, Saboura Dolati Pish,Khoramdel, Mehdi Korean Mathematical Society 2014 대한수학회지 Vol.51 No.1
An element r of a commutative semiring R with identity is said to be identity-summand if there exists $1{\neq}a{\in}R$ such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by ${\Gamma}(R)$. It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph ${\Gamma}(R)$ are studied.
Zero-divisor graphs with respect to primal and weakly primal ideals
Shahabaddin Ebrahimi Atani,Ahamd Yousefian Darani 대한수학회 2009 대한수학회지 Vol.46 No.2
We consider zero-divisor graphs with respect to primal, non-primal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Γ_{I} (R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization. We consider zero-divisor graphs with respect to primal, non-primal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Γ_{I} (R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.
MULTIPLICATION MODULES OVER PULLBACK RINGS (I)
ATANI, SHAHABADDIN EBRAHIMI,LEE, SANG CHEOL 호남수학회 2006 호남수학학술지 Vol.28 No.1
First, we give a complete description of the multiplication modules over local Dedekind domains. Second, if R is the pullback ring of two local Dedekind domains over a common factor field then we give a complete description of separated multiplication modules over R.
THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS
Shahabaddin Ebrahimi Atani,Saboura Dolati Pish Hesari,Mehdi Khoramdel 대한수학회 2014 대한수학회지 Vol.51 No.1
An element r of a commutative semiring R with identity is said to be identity-summand if there exists 1 ≠ α ∈ R such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by Γ(R). It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph Γ(R) are studied.
ZERO-DIVISOR GRAPHS WITH RESPECT TO PRIMAL AND WEAKLY PRIMAL IDEALS
Atani, Shahabaddin Ebrahimi,Darani, Ahamd Yousefian Korean Mathematical Society 2009 대한수학회지 Vol.46 No.2
We consider zero-divisor graphs with respect to primal, nonprimal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ringtheoretic properties of R and the graph-theoretic properties of ${\Gamma}_I(R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL
Atani, Shahabaddin Ebrahimi,Hesari, Saboura Dolati Pish,Khoramdel, Mehdi Korean Mathematical Society 2015 대한수학회지 Vol.52 No.1
Let R be a semiring, I a strong co-ideal of R and S(I) the set of all elements of R which are not prime to I. In this paper we investigate some interesting properties of S(I) and introduce the total identity-summand graph of a semiring R with respect to a co-ideal I. It is the graph with all elements of R as vertices and for distinct x, $y{\in}R$, the vertices x and y are adjacent if and only if $xy{\in}S(I)$.
STRONGLY IRREDUCIBLE SUBMODULES
ATANI, SHAHABADDIN EBRAHIMI Korean Mathematical Society 2005 대한수학회보 Vol.42 No.1
This paper is motivated by the results in [6]. We study some properties of strongly irreducible submodules of a module. In fact, our objective is to investigate strongly irreducible modules and to examine in particular when sub modules of a module are strongly irreducible. For example, we show that prime submodules of a multiplication module are strongly irreducible, and a characterization is given of a multiplication module over a Noetherian ring which contain a non-prime strongly irreducible submodule.
THE PRODUCT OF MULTIPLICATION SUBMODULES
ATANI, SHAHABADDIN EBRAHIMI The Honam Mathematical Society 2005 호남수학학술지 Vol.27 No.1
Let R be a commutative ring with non-zero identity. This paper is devoted to the study some of properties of the product of submodules of a multiplication module. Suppose N is a submodule of a multiplication R-module M. We give a condition which allows us to determine whether N is finitely generated when we assume some power of N is finitely generated.