منابع مشابه
T-Rough (Prime, Primary) Ideal and T-Rough Fuzzy (Prime, Primary) Ideal on Commutative Rings
The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...
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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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It is known that the theory K of commutative regular rings with identity has a model completion K . We show that there exists a countable model of K which has no prime extension to a model of K'. If K and K ate theories in a first order language L, then K is said to be a model completion of K if K extends K, every model of K can be embedded in a model of K , and for any model A of K and models ...
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Acknowledgments I would like to begin by thanking my advisor, Professor Alexander Diesl, for his encouragement and excitement for my research. He has always remained supportive and interested in my work, and his many questions have kept me motivated and excited about my project. I would like to thank him as well for being understanding about my silly questions, helping me piece apart my convolu...
متن کاملFinitely Generated Annihilating-Ideal Graph of Commutative Rings
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: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1969-0251026-x