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Some functional identities arising from derivations

Lahcen Oukhtite|Abdellah Mamouni|Mohammed Zerra
대한수학회 (The Korean Mathematical Society)|2023.01|대한수학회논문집 (Communications of the KMS)|제38권 제1호|pp. 79-87|DOI 10.4134/CKMS.c220004

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키워드

Prime ringderivationscommutativityprime ideal
주제분류수학

초록

This paper considers some functional identities related to derivations of a ring $R$ and their action on the centre of $R/P$ where $P$ is a prime ideal of $R.$ It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.

Abstract

This paper considers some functional identities related to derivations of a ring $R$ and their action on the centre of $R/P$ where $P$ is a prime ideal of $R.$ It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.

참고문헌 (16)

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  3. Karim Bouchannafa, "Relationship between the structure of a quotient ring and the behavior of certain additive mappings", 대한수학회논문집, 37(2), pp.359~370 (2022), 대한수학회[DOI]
  4. T. Creedon, "Derivations and prime ideals", Math. Proc. R. Ir. Acad, 98A(2), pp.223~225 (1998)
  5. Hajar El Mir, "Commutativity with algebraic identities involving prime ideals", 대한수학회논문집, 35(3), pp.723~731 (2020), 대한수학회[DOI]
  6. I. N. Herstein, "Topics in Ring Theory" (1969), University of Chicago Press
  7. I. N. Herstein, "Rings with Involution" (1976), University of Chicago Press
  8. I. N. Herstein, "A note on derivations", Canad. Math. Bull, 21(3), pp.369~370 (1978)[DOI]
  9. I. N. Herstein, "A note on derivations. II", Canad. Math. Bull, 22(4), pp.509~511 (1979)[DOI]
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  11. T. -K. Lee, "Generalized derivations of left faithful rings", Comm. Algebra, 27(8), pp.4057~4073 (1999)[DOI]
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  13. A. Mamouni, "New classes of endomorphisms and some classi cation theorems", Comm. Algebra, 48(1), pp.71~82 (2020)[DOI]
  14. A. Mamouni, "On derivations involving prime ideals and commutativity in rings", S~ao Paulo J. Math. Sci, 14(2), pp.675~688 (2020)[DOI]
  15. L. Oukhtite, "Generalized derivations centralizing on Jordan ideals of rings with involution", Turkish J. Math, 38(2), pp.225~232 (2014)[DOI]
  16. E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)[DOI]

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