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MULTIPLICATIVE SET OF IDEMPOTENTS IN A SEMIPERFECT RING

  • Park, Sang-Won (Department of Mathematics Dong-A University) ;
  • Han, Jun-Cheol (Department of Mathematics Education Pusan National University)
  • Received : 2010.03.23
  • Published : 2011.09.30

Abstract

Let R be a ring with identity 1, I(R) be the set of all idempotents in R and G be the group of all units of R. In this paper, we show that for any semiperfect ring R in which 2 = 1+1 is a unit, I(R) is closed under multiplication if and only if R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication and eGe is contained in the group of units of eRe. In particular, for a left Artinian ring in which 2 is a unit, R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication.

Keywords

References

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Cited by

  1. Multiplicative Sets of Primitive Idempotents and Primitive Ideals vol.44, pp.1, 2016, https://doi.org/10.1080/00927872.2014.944264