Kyungpook Mathematical Journal

  • 제51권3호
  • /
  • Pages.283-291
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  • 2011
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On a Class of Semicommutative Rings

  • 투고 : 2010.05.05
  • 심사 : 2011.03.15
  • 발행 : 2011.09.23
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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 ${\in}$ R, ab = 0 implies arb is a central element of R for each r ${\in}$ R. We prove that some results on semicommutative rings can be extended to central semicommutative rings for this general settings.

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참고문헌

  1. N. Agayev and A. Harmanci, On Semicommutative Modules and Rings, Kyungpook Math. J., 47(1)(2007), 21-30.
  2. M. Baser and N. Agayev, On Reduced and Semicommutative Modules, Turk. J. Math., 30(2006), 285-291.
  3. Y. Hirano, Some Studies of Strongly $\pi$-Regular Rings, Math. J. Okayama Univ., 20(2)(1978), 141-149.
  4. C. Y. Hong, N. K. Lim and T. K. Kwak, Extensions of Generalized Reduced Rings, Alg. Coll., 12(2)(2005), 229-240. https://doi.org/10.1142/S1005386705000222
  5. S. U. Hwang, C. H. Jeon and K. S. Park, A Generalization of Insertion of Factors Property, Bull. Korean Math. Soc., 44(1)(2007), 87-94. https://doi.org/10.4134/BKMS.2007.44.1.087
  6. N. K. Kim and Y. Lee, Extensions of Reversible Rings, J. Pure and Applied Alg., 167(2002), 37-52. https://doi.org/10.1016/S0022-4049(01)00149-9
  7. L. Liang, L. Wang and Z. Liu, On a Generalization of Semicommutative Rings, Taiwanese Journal of Mathematics, 11(5)(2007), 1359-1368. https://doi.org/10.11650/twjm/1500404869
  8. G. Shin, Prime ideals and Sheaf Represantation of a Pseudo Symmetric ring, Transactions of the American Mathematical Society, 184(1973), 43-69. https://doi.org/10.1090/S0002-9947-1973-0338058-9

피인용 문헌

  1. ON A RING PROPERTY GENERALIZING POWER-ARMENDARIZ AND CENTRAL ARMENDARIZ RINGS vol.23, pp.3, 2015, https://doi.org/10.11568/kjm.2015.23.3.337
  2. On some classes of reflexive rings vol.08, pp.01, 2015, https://doi.org/10.1142/S1793557115500035
  3. Central semicommutative rings vol.45, pp.1, 2014, https://doi.org/10.1007/s13226-014-0048-9
  4. ON PROPERTIES RELATED TO REVERSIBLE RINGS vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.247
  5. Further results on central Armendariz rings vol.16, pp.10, 2017, https://doi.org/10.1142/S0219498817501948