非交换环的弱素和弱完全素理想

IF 0.5 Q3 MATHEMATICS

International Electronic Journal of Algebra Pub Date : 2020-07-14 DOI:10.24330/ieja.768127

N. Groenewald

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引用次数: 7

摘要

Anderson-Smith研究了具有恒等式的交换环的弱素理想。Hirano、Poon和Tsutsui研究了环的结构，其中每个理想对环都是弱素数，不一定是交换的。在这个注记中，我们给出了非对易环中弱素理想的更多性质。我们引入了理想的弱素数根的概念。我们开始研究弱完全素理想，并研究每个适当理想都是弱完全素的环。

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WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS

Anderson-Smith studied weakly prime ideals for a commutative ring with identity. Hirano, Poon and Tsutsui studied the structure of a ring in which every ideal is weakly prime for rings, not necessarily commutative. In this note we give some more properties of weakly prime ideals in noncommutative rings. We introduce the notion of a weakly prime radical of an ideal. We initiate the study of weakly completely prime ideals and investigate rings for which every proper ideal is weakly completely prime.

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来源期刊

International Electronic Journal of Algebra MATHEMATICS-

CiteScore

0.90

自引率

16.70%

发文量

审稿时长

36 weeks

期刊介绍： The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.