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arXiv · 1905.01476

A Generalization of Reflexive Rings

M. B. Calci·H. Chen·S. Halicioglu
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Abstract

In this paper, we introduce a class of rings which is a generalization of reflexive rings and $J$-reversible rings. Let $R$ be a ring with identity and $J(R)$ denote the Jacobson radical of $R$. A ring $R$ is called {\it $J$-reflexive} if for any $a$, $b \in R$, $aRb = 0$ implies $bRa \subseteq J(R)$. We give some characterizations of a $J$-reflexive ring. We prove that some results of reflexive rings can be extended to $J$-reflexive rings for this general setting. We conclude some relations between $J$-reflexive rings and some related rings. We investigate some extensions of a ring which satisfies the $J$-reflexive property and we show that the $J$-reflexive property is Morita invariant.

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M. B. Calci, H. Chen, S. Halicioglu. 2019-05-04. A Generalization of Reflexive Rings. https://arxiv.org/abs/1905.01476

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