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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)
  • Received : 2018.10.30
  • Accepted : 2019.02.07
  • Published : 2019.09.30

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

Acknowledgement

Supported by : National Natural Science Foundation of China

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