Reflexive property on nil ideals

Kheradmand Mehdi; Kim Hong Kee; Kwak Tai KeunLee Yang

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Reflexive property on nil ideals

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We in this note consider the reflexive ring property on nil ideals, introducing the concept of a nil-reflexive ring as a generalization of the reflexive ring property. We will call a ring R nil-reflexive if IJ = 0 implies JI = 0 for nil ideals I, J of R. The polynomial and the power series rings over a right Noetherian ring (or an NI ring) R are shown to be nil-reflexive if (aRb)(2) = 0 implies aRb = 0 for all a, b is an element of N(R). We further investigate the structure of nil-reflexive rings, related to various sorts of ring extensions which have roles in ring theory.

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来源
《Journal of algebra and its applications》 |2017年第2期|共19页
作者
Kheradmand Mehdi; Kim Hong Kee; Kwak Tai KeunLee Yang;
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作者单位

Isfahan Univ Technol, Dept Math Sci, Esfahan, Iran;

Gyeongsang Natl Univ, Dept Math, Jinju 52828, South Korea;

Daejin Univ, Dept Math, Pochon 11159, South KoreaPusan Natl Univ, Dept Math Educ, Pusan 46241, South Korea;

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正文语种英语
中图分类代数、数论、组合理论;
关键词
Nil-reflexive ring; nil ideal; matrix ring; polynomial ring; power series ring; right quotient ring;

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Reflexive property on nil ideals

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