Reflexive property on idempotents
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 1957-1972
Printed November 1, 2013
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
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