Received March 6, 2022. Published online April 5, 2023.
Abstract: 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 $J$-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.
Affiliations: Mete Burak Çalcı (corresponding author), Tübitak-Bilgem, Informatics and Information Security Research Center, Tübitak Gebze Yerleşkesi, Gebze, Turkey, e-mail: firstname.lastname@example.org; Huanyin Chen, Department of Mathematics, Hangzhou Normal University, No. 2318, Yuhangtang Road, Yuhang District, 311121 Hangzhou, P.R. China, e-mail: email@example.com; Sait Halıcıoğlu, Department of Mathematics, Faculty of Sciences, Ankara University, Dögol Caddesi 06100, Ankara, Turkey, e-mail: firstname.lastname@example.org