The Graph of Annihilating Ideals
نویسندگان
چکیده
منابع مشابه
Annihilating Ideals and Tilting Functors
We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known in the case of a simple Lie algebra.
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Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...
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The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
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Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where $mathbb{P}(R)$ is...
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Let $R$ be a commutative ring and $mathbb{A}(R)$ be the set of all ideals with non-zero annihilators. Assume that $mathbb{A}^*(R)=mathbb{A}(R)diagdown {0}$ and $mathbb{F}(R)$ denote the set of all finitely generated ideals of $R$. In this paper, we introduce and investigate the {it finitely generated subgraph} of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_F(R)$. It is the (undi...
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ژورنال
عنوان ژورنال: AL-Rafidain Journal of Computer Sciences and Mathematics
سال: 2018
ISSN: 2311-7990
DOI: 10.33899/csmj.2018.163569