Korean Journal of Mathematics

  • 제29권3호
  • /
  • Pages.483-492
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  • 2021
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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REDUCED PROPERTY OVER IDEMPOTENTS

  • Kwak, Tai Keun (Department of Mathematics, Daejin University) ;
  • Lee, Yang (Department of Mathematics, Yanbian University and Institute of Basic Science, Daejin University) ;
  • Seo, Young Joo (Department of Mathematics, Daejin University)
  • 투고 : 2021.02.06
  • 심사 : 2021.07.11
  • 발행 : 2021.09.30
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초록

This article concerns the property that for any element a in a ring, if a2n = an for some n ≥ 2 then a2 = a. The class of rings with this property is large, but there also exist many kinds of rings without that, for example, rings of characteristic ≠2 and finite fields of characteristic ≥ 3. Rings with such a property is called reduced-over-idempotent. The study of reduced-over-idempotent rings is based on the fact that the characteristic is 2 and every nonzero non-identity element generates an infinite multiplicative semigroup without identity. It is proved that the reduced-over-idempotent property pass to polynomial rings, and we provide power series rings with a partial affirmative argument. It is also proved that every finitely generated subring of a locally finite reduced-over-idempotent ring is isomorphic to a finite direct product of copies of the prime field {0, 1}. A method to construct reduced-over-idempotent fields is also provided.

키워드

과제정보

The authors thank the referee deeply for very careful reading of the manuscript and valuable suggestions in depth that improved the paper by much.

참고문헌

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