Primary ideal representations in non-commutative rings
نویسندگان
چکیده
منابع مشابه
Exact annihilating-ideal graph of commutative rings
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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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...
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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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Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Gröbner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitel...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1963
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(63)50006-7