East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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I-SEMIREGULAR RINGS

  • Han, Juncheol (Department of Mathematics Education, Pusan National University) ;
  • Sim, Hyo-Seob (Department of Applied Mathematics, Pukyong National University)
  • Received : 2020.02.13
  • Accepted : 2020.04.09
  • Published : 2020.05.31
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Abstract

Let R be a ring with unity, and let I be an ideal of R. Then R is called I-semiregular if for every a ∈ R there exists b ∈ R such that ab is an idempotent of R and a - aba ∈ I. In this paper, basic properties of I-semiregularity are investigated, and some equivalent conditions to the primitivity of e are observed for an idempotent e of an I-semiregular ring R such that I∩eR = (0). For an abelian regular ring R with the ascending chain condition on annihilators of idempotents of R, it is shown that R is isomorphic to a direct product of a finite number of division rings, as a consequence of the observations.

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References

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