Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(6): 1957-1972

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.1957

Copyright © The Korean Mathematical Society.

Reflexive property on idempotents

Tai Keun Kwak and Yang Lee

Daejin University, Pusan National University

Abstract

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization.It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.

Keywords: reflexive property, reflexive-idempotents-property (RIP), polynomial ring, Dorroh extension, minimal RIP ring

MSC numbers: 16S99, 16U80