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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Journal of Algebra and Related Topics
- نوع مقاله: Journal Article
- کلمات کلیدی: Maximal non-prime ideal,maximal non-maximal ideal,maximal non-primary ideal,maximal non-irreducible ideal
- چکیده:
- چکیده انگلیسی: The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $Ineq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$, $I$ is maximal with respect to the property of being not a prime ideal. The concept of maximal non-maximal ideal and maximal non-primary ideal of a ring can be similarly defined. The aim of this article is to characterize ideals $I$ of a ring $R$ such that $I$ is a maximal non-prime (respectively, a maximal non maximal, a maximal non-primary) ideal of $R$.
- انتشار مقاله: 22-03-1394
- نویسندگان: S. Visweswaran,A. Parmar
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: N-prime of $(0)$,B-prime of $(0)$,complement of the annihilating-ideal graph of a commutative ring,vertex cut and cut vertex of a connected graph
- چکیده:
- چکیده انگلیسی: The rings considered in this article are commutative with identity which admit at least two nonzero annihilating ideals. Let $R$ be a ring. Let $mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $mathbb{A}(R)^{*} = mathbb{A}(R)backslash {(0)}$. The annihilating-ideal graph of $R$, denoted by $mathbb{AG}(R)$ is an undirected simple graph whose vertex set is $mathbb{A}(R)^{*}$ and distinct vertices $I, J$ are joined by an edge in this graph if and only if $IJ = (0)$. The aim of this article is to classify rings $R$ such that $(mathbb{AG}(R))^{c}$ ( that is, the complement of $mathbb{AG}(R)$) is connected and admits a cut vertex.
- انتشار مقاله: 21-01-1395
- نویسندگان: S. VISWESWARAN,A. PARMAR
- مشاهده