Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

On a Class of Semicommutative Rings

  • Received : 2010.05.05
  • Accepted : 2011.03.15
  • Published : 2011.09.23
Download PDF
⟨ Previous Next ⟩

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 ${\in}$ 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.

Keywords

References

  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

Cited by

  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