Bulletin of the Korean Mathematical Society (대한수학회보)

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REFLEXIVE PROPERTY ON IDEMPOTENTS

  • Kwak, Tai Keun (Department of Mathematics Daejin University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University)
  • Received : 2012.07.19
  • Published : 2013.11.30
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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.

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References

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