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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)

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