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http://dx.doi.org/10.4134/BKMS.b180759

ON REVERSIBILITY RELATED TO IDEMPOTENTS  

Jung, Da Woon (Finance Fishery Manufacture Industrial Mathematics Center on Big Data Pusan National University)
Lee, Chang Ik (Department of Mathematics Pusan National University)
Lee, Yang (Department of Mathematics Yanbian University)
Park, Sangwon (Department of Mathematics Dong-A University)
Ryu, Sung Ju (Department of Mathematics Pusan National University)
Sung, Hyo Jin (Department of Mathematics Pusan National University)
Yun, Sang Jo (Department of Mathematics Dong-A University)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 993-1006 More about this Journal
Abstract
This article concerns a ring property which preserves the reversibility of elements at nonzero idempotents. A ring R shall be said to be 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;
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Times Cited By KSCI : 1  (Citation Analysis)
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