2019/05/04 by Mete Burak Calci, H. Chen, Calci, M. B. +3
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1905.01476
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 ∈ R, aRb = 0 implies bRa ⊆ 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.