- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 On reversibility related to idempotents Bull. Korean Math. Soc. 2019 Vol. 56, No. 4, 993-1006 https://doi.org/10.4134/BKMS.b180759Published online July 31, 2019 Da Woon Jung, Chang Ik Lee, Yang Lee, Sangwon Park, Sung Ju Ryu, Hyo Jin Sung, Sang Jo Yun Pusan National University; Pusan National University; Daejin University; Dong-A University; Pusan National University; Pusan National University; Dong-A University Abstract : This article concerns a ring property which preserves the reversibility of elements at nonzero idempotents. A ring $R$ shall be said to be {\it quasi-reversible} if $0\neq ab\in I(R)$ for $a, b\in R$ implies $ba\in I(R)$, where $I(R)$ is the set of all idempotents in $R$. We investigate the quasi-reversibility of $2$ by $2$ full and upper triangular matrix rings over various kinds of reversible rings, concluding that the quasi-reversibility is a proper generalization of the reversibility. It is shown that the quasi-reversibility does not pass to polynomial rings. The structure of Abelian rings is also observed in relation with reversibility and quasi-reversibility. Keywords : quasi-reversible ring, Abelian ring, reversible ring, matrix ring, polynomial ring, NI ring MSC numbers : 16U80, 16S36, 16S50 Full-Text :