[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b181038

REVERSIBLE AND PSEUDO-REVERSIBLE RINGS

Huang, Juan (Department of Mathematics Yanbian University)
Jin, Hai-lan (Department of Mathematics Yanbian University)
Lee, Yang (Department of Mathematics Yanbian University)
Piao, Zhelin (Department of Mathematics Yanbian University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.5, 2019 , pp. 1257-1272 More about this Journal

Abstract

This article concerns the structure of idempotents in reversible and pseudo-reversible rings in relation with various sorts of ring extensions. It is known that a ring R is reversible if and only if $ab{\in}I(R)$ for $a,b{\in}R$ implies ab = ba; and a ring R shall be said to be pseudoreversible if $0{\neq}ab{\in}I(R)$ for $a,b{\in}R$ implies ab = ba, where I(R) is the set of all idempotents in R. Pseudo-reversible is seated between reversible and quasi-reversible. It is proved that the reversibility, pseudoreversibility, and quasi-reversibility are equivalent in Dorroh extensions and direct products. Dorroh extensions are also used to construct several sorts of rings which are necessary in the process.

Keywords

pseudo-reversible ring; reversible ring; Dorroh extension; Abelian ring; quasi-reversible ring; direct product; free algebra; matrix ring; polynomial ring;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

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