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Journals / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 5

Some commutativity criteria involving endomorphism conditions on prime ideals

L. OUKHTİTE
Abdellah MAMOUNI
Mohammed ZERRA
Pages
1280–1287
Publication Date
2022-10-01
DOI
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⚡ TL;DR(Too Long; Didn't Read)

In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring $R/P$ by endomorphisms of $R$ satisfying some algebraic identities involving the prime ideal $P.$ Some well-known results concerning the commutativity of prime (semi-prime) rings have been improved.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring $R/P$ by endomorphisms of $R$ satisfying some algebraic identities involving the prime ideal $P.$ Some well-known results concerning the commutativity of prime (semi-prime) rings have been improved.
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Key Findings & Data:In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring $R/P$ by endomorphisms of $R$ satisfying some algebraic identities involving the prime ideal $P.$ Some well-known results concerning the commutativity of prime (semi-prime) rings have been improved.
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Conclusion & Impact:In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring $R/P$ by endomorphisms of $R$ satisfying some algebraic identities involving the prime ideal $P.$ Some well-known results concerning the commutativity of prime (semi-prime) rings have been improved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:prime ideals · commutativity · endomorphisms

Abstract

In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring $R/P$ by endomorphisms of $R$ satisfying some algebraic identities involving the prime ideal $P.$ Some well-known results concerning the commutativity of prime (semi-prime) rings have been improved.

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Cite This Article

OUKHTİTE, L., MAMOUNI, A., ZERRA, M. (2022). Some commutativity criteria involving endomorphism conditions on prime ideals. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 5, 1280–1287. https://ajindex.com/articles/669150

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References (14)

  1. C.M. Anwar and A.B. Thaheem, Centralizing mappings and derivations on semiprime rings, Demonstratio Math. 37(2), 285-292, 2004
  2. H.E. Bell and M.N. Daif, On commutativity and strong commutativity-preserving maps, Canad. Math. Bull. 37(4), 443-447, 1994
  3. I.N. Herstein, A note on derivations, Canad. Math. Bull. 21, 369-370, 1978
  4. S. Huang, O. Golbas, and E. Koc, On centralizing and strong commutativity preserving maps of semiprime rings, Ukrainian Math. J. 67(2), 323-331, 2015
  5. C. Lanski, Differential identities, Lie ideals and Posner’s theorems, Pacific J. Math. 134(2), 275-297, 1988
  6. A. Mamouni, L. Oukhtite and B. Nejjar, Differential identities on prime rings with involution, J. Algebra Appl. 17(9), 1850163, 2018
  7. A. Mamouni, L. Oukhtite and B. Nejjar, On ∗-semiderivations and ∗-generalized semiderivations, J. Algebra Appl. 16(4), 1750075, 2017
  8. A. Mamouni, L. Oukhtite and M. Zerra, On derivations involving prime ideals and commutativity in rings, São Paulo J. Math. Sci. 14(2), 675-688, 2020
  9. A. Mamouni, L. Oukhtite and M. Zerra, Prime ideals and generalized derivations with central values on rings, Rend. Circ. Mat. Palermo (2), 70(3), 1645, 2021
  10. J. Mayne, Centralizing automorphisms of prime rings, Can. Math. Bull. 19(1), 113- 115, 1976
  11. B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Commutativity theorems in rings with involution, Comm. Algebra 45(2), 698-702, 2017
  12. L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math. 38(2), 225-232, 2014
  13. L. Oukhtite, A. Mamouni and M. Ashraf, Commutativity theorems for rings with differential identities on Jordan ideals, Comment. Math. Univ. Carolin. 54 (4), 447- 457, 2013
  14. E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093-1100, 1957.