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On a Class of Semicommutative Rings

Abdullah Harmanci|Tahire Özen|Nazim Agayev
경북대학교 자연과학대학 수학과|2011.09|Kyungpook Mathematical Journal|제51권 제3호|pp. 283-291

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참고문헌

키워드

semicommutative ringsweakly semicommutative ringsreduced rings
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초록

In this paper, a generalization of the class of semicommutative rings is investigated. A ring R is called central semicommutative if for any a, b ∈ R, ab = 0 implies arb is a central element of R for each r ∈ R. We prove that some results on semicommutative rings can be extended to central semicommutative rings for this general settings.

Abstract

In this paper, a generalization of the class of semicommutative rings is investigated. A ring R is called central semicommutative if for any a, b ∈ R, ab = 0 implies arb is a central element of R for each r ∈ R. We prove that some results on semicommutative rings can be extended to central semicommutative rings for this general settings.

참고문헌 (8)

  1. Nazim Agayev, "On Semicommutative Modules and Rings", Kyungpook Mathematical Journal, 47(1), pp.21~30 (2007), 경북대학교 자연과학대학 수학과
  2. M. Baser, "On Reduced and Semicommutative Modules", Turk. J. Math, 30, pp.285~291 (2006)
  3. Y. Hirano, "Some Studies of Strongly π-Regular Rings", Math. J. Okayama Univ, 20(2), pp.141~149 (1978)
  4. C. Y. Hong, "Extensions of Generalized Reduced Rings", Alg. Coll, 12(2), pp.229~240 (2005)
  5. Seo Un Hwang, "A generalization of Insertion-of-factors-property", 대한수학회보, 44(1), pp.87~94 (2007), 대한수학회
  6. N. K. Kim, "Extensions of Reversible Rings", J. Pure and Applied Alg, 167, pp.37~52 (2002)
  7. L. Liang, "On a Generalization of Semicommutative Rings", Tai-wanese Journal of Mathematics, 11(5), pp.1359~1368 (2007)
  8. G. Shin, "Prime ideals and Sheaf Represantation of a Pseudo Symmetric ring", Trans-actions of the American Mathematical Society, 184, pp.43~69 (1973)

관련 논문AI추천

Generalized semicommutative rings and their extensions곽태근, Abdullah Harmanci, Muhittin Baser대한수학회 · 대한수학회보2008 · 제45권 제2호Commutativity Criteria for a Factor Ring R/P Arising from P-CentralizersKarim Bouchannafa, Lahcen Oukhtite, My Abdallah Idrissi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제4호On a ring property generalizing power-Armendariz and central Armendariz rings이양, 김진아, 김홍기, 남상복, 류성주, 서연숙, 성효진, 윤상조, 이창익, 정다운, 차호준강원경기수학회 · 한국수학논문집2015 · 제23권 제3호Weakly Semicommutative Rings and Strongly Regular RingsJunchao Wei, Long Wang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호On partial-Armendariz rings남상복, 윤상조, Zhelin Piao대한수학회 · 대한수학회논문집2019 · 제34권 제3호On quasi-commutative rings이양, 김병옥, 김홍기, 남상복, 류성주, 성효진, 윤상조, 정다운대한수학회 · 대한수학회지2016 · 제53권 제2호

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