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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2020.1
- 수록면
- 73 - 79 (7page)
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A ring R is called generalized regular if for every nonzero x in R there exists y in R such that xy is a nonzero idempotent. In this paper, we observe some equivalent conditions for the generalized regular rings that are abelian in terms of idempotents, and we also investigate the primitivity of an idempotent for such a ring. By using the investigation, we characterize such a kind of rings that are noetherian by showing that an abelian generalized regular ring R is noetherian if and only if R is isomorphic to a direct product of finitely many division rings. We also observe some interesting consequences of our results.
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참고문헌 (6)
참고문헌 신청
D. D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. in Algebra 27:2847~2852
한준철 / 2016 / On idempotents in relation with regularity / 대한수학회지 53(1):217~232
한준철 / 2018 / Rings With The Symmetric Property for Idempotent-Products / East Asian Mathematical Journal 34(5):615~621
C. Huh / 2005 / Basic examples and extensions of symmetric rings / J. Pure and Applied Algebra 202:154~167
정다운 / 2015 / On properties related to reversible rings / 대한수학회보 52(1):247~261
한준철 / 2016 / On idempotents in relation with regularity / 대한수학회지 53(1):217~232
한준철 / 2018 / Rings With The Symmetric Property for Idempotent-Products / East Asian Mathematical Journal 34(5):615~621
C. Huh / 2005 / Basic examples and extensions of symmetric rings / J. Pure and Applied Algebra 202:154~167
정다운 / 2015 / On properties related to reversible rings / 대한수학회보 52(1):247~261
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