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REDUCED MODULES AND STRONGLY REGULAR RINGS

김두원|허찬|천정수
영남수학회 (Youngnam Mathematical Society)|2017.01|East Asian Mathematical Journal|제33권 제1호|pp. 75-81|DOI http://dx.doi.org/10.7858/eamj.2017.008

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참고문헌

키워드

Reduced rings and modulesRegular and strongly regular rings
주제분류수학

초록

It is a well-known fact that a ring R is regular if and only if every left R-modules is flat. In this article we prove that a ring R is strongly regular if and only if every left R-modules is reduced if and only if every left-R modules is quasi-reduced.

Abstract

It is a well-known fact that a ring R is regular if and only if every left R-modules is flat. In this article we prove that a ring R is strongly regular if and only if every left R-modules is reduced if and only if every left-R modules is quasi-reduced.

참고문헌 (5)

  1. G.Azumaya, "Strongly -regular Rings", Journal of Fac.Sci.Hokkaido Univ. Ser. I, 13, pp.34~39 (1954)
  2. A.Buhpang, "Semicommutative modules and Armendariz modules", Arab Journal of Math. Sci, 18, pp.53~65 (2002)
  3. K.R.Goordearl, "Von Neumann Regular Rings" (1979), Pitman Publ
  4. J.Lambek, "Lectures on rings and modules" (1966), Blaisdell Publishing Company
  5. C.P.Zhang, "α-Skew Armendariz and α-Semicommutative modules", Taiwan.J. Of Math, 12(2), pp.473~486 (2008)

관련 논문AI추천

On Left SF-Rings and Strongly Regular RingsArdeline Mary Buhphang, Tikaram Subedi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호Weakly np- Injective Rings and Weakly C2 RingsJianhua Chen, Junchao Wei경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2011 · 제51권 제1호SOME RESULTS ON REDUCIBILITY AND STRONG REDUCIBILITY조용욱영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호Weakly Semicommutative Rings and Strongly Regular RingsJunchao Wei, Long Wang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호Rings close to semiregular이양, A. Cigdem Ozcan, Pinar Aydogdu대한수학회 · 대한수학회지2012 · 제49권 제3호Rings Whose Simple Singular Modules are PS-InjectiveLunqun Ouyang, Yueming Xiang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제3호

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