Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON IDEMPOTENTS IN RELATION WITH REGULARITY

  • HAN, JUNCHEOL (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY) ;
  • LEE, YANG (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY) ;
  • PARK, SANGWON (DEPARTMENT OF MATHEMATICS DONG-A UNIVERSITY) ;
  • SUNG, HYO JIN (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY) ;
  • YUN, SANG JO (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
  • Received : 2014.10.31
  • Published : 2016.01.01
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Abstract

We make a study of two generalizations of regular rings, concentrating our attention on the structure of idempotents. A ring R is said to be right attaching-idempotent if for $a{\in}R$ there exists $0{\neq}b{\in}R$ such that ab is an idempotent. Next R is said to be generalized regular if for $0{\neq}a{\in}R$ there exist nonzero $b{\in}R$ such that ab is a nonzero idempotent. It is first checked that generalized regular is left-right symmetric but right attaching-idempotent is not. The generalized regularity is shown to be a Morita invariant property. More structural properties of these two concepts are also investigated.

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Acknowledgement

Supported by : Pusan National University

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