Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Commutativity Criteria for a Factor Ring R/P Arising from P-Centralizers

  • Lahcen Oukhtite (Department of Mathematics, Faculty of Sciences and Technology, S. M. Ben Abdellah University) ;
  • Karim Bouchannafa (Department of Mathematics, Faculty of Sciences and Technology, S. M. Ben Abdellah University) ;
  • My Abdallah Idrissi (Department of Mathematics and informatics, Polydisciplinary Faculty)
  • Received : 2022.09.05
  • Accepted : 2023.03.21
  • Published : 2023.12.31
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Abstract

In this paper we consider a more general class of centralizers called I-centralizers. More precisely, given a prime ideal P of an arbitrary ring R we establish a connection between certain algebraic identities involving a pair of P-left centralizers and the structure of the factor ring R/P.

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References

  1. A. Abbasi, M. S. Khan and M. R. Mozumder, On commutativity and centralizers of prime ring with involution, Thai J. Math., 20(3)(2022), 1329-1335.
  2. A. Z. Ansari and F. Shujat, Additive mappings on semiprime rings functioning as centralizers, Aust. J. Math. Anal. Appl., 19(2)(2022), Art. 11, 9 pp.
  3. M. Ashraf and S. Ali, On left multipliers and the commutativity of prime rings, Demonstratio Math., 41(4)(2008), 763-771. https://doi.org/10.1515/dema-2008-0404
  4. N. Aydin, A note on generalized derivations of prime rings, Int. J. Algebra, 5(2011), 17-23.
  5. K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with generalized identities, Monogr. Textbooks Pure Appl. Math. 196, Marcel Dekker, Inc., New York, 1996, xiv+522 pp.
  6. M. Fosner and B. Marcen, A new equation related to two-sided centralizers in prime rings, Aequationes Math., 96(6)(2022), 1207-1219. https://doi.org/10.1007/s00010-022-00904-3
  7. M. Fosner, B. Marcen and J. Vukman, On functional equation related to (m, n)-Jordan centralizers in prime rings, Bull. Malays. Math. Sci. Soc., 42(6)(2019), 3131-3147. https://doi.org/10.1007/s40840-018-0650-9
  8. L. Oukhtite, Left multipliers and Jordan ideals in rings with involution, Afr. Diaspora J. Math., 11(1)(2011), 24-28.