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Identities in a Prime Ideal of a Ring Involving Generalized Derivations
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In this paper, we will study the structure of the quotient ring R/P of an arbitrary ring R by a prime ideal P. We do so using differential identities involving generalized derivations of R. We enrich our results with examples that show the necessity of their assumptions.
Abstract
In this paper, we will study the structure of the quotient ring R/P of an arbitrary ring R by a prime ideal P. We do so using differential identities involving generalized derivations of R. We enrich our results with examples that show the necessity of their assumptions.
참고문헌 (8)
- L. K. Ardakani, "On derivations of prime and semi-prime Gamma rings", Bol. Soc. Param. Mat, 37(2), pp.155~164 (2019)
- H. E. Bell, "Rings in which derivations satisfy certain algebraic conditions", Acta. Math. Hungar, 53, pp.339~346 (1989)
- B. Davvaz, "A note on automorphisms of Lie ideals in prime rings", Math. Slovaca, 68(5), pp.1223~1229 (2018)
- A. Mamouni, "On derivations involving prime ideals and commutativity in rings", S˜ao Paulo J. Math. Sci, 14, pp.675~688 (2020)
- Hajar El Mir, "Commutativity with algebraic identities involving prime ideals", 대한수학회논문집, 35(3), pp.723~731 (2020), 대한수학회[DOI]
- N. Rehman, "On generalized derivations as homomorphisms and anti-homomorphisms", Glas. Mat, 39(59), pp.27~30 (2004)
- N. Rehman, "Action of prime ideals on generalized derivations-I", ~
- Gurninder S. Sandhu, "On generalized derivations and Jordan ideals of prime rings", Rendiconti del Circolo Matematico di Palermo Series 2, 70(1), pp.227~233 (2021), Springer Science and Business Media LLC[DOI]
관련 논문AI추천
Commutativity with algebraic identities involving prime idealsAbdellah Mamouni, Hajar El Mir, Lahcen Oukhtite대한수학회 · 대한수학회논문집2020 · 제35권 제3호Relationship between the structure of a quotient ring and the behavior of certain additive mappingsKarim Bouchannafa, Lahcen Oukhtite, Moulay Abdallah Idrissi대한수학회 · 대한수학회논문집2022 · 제37권 제2호RELATIONSHIP BETWEEN THE STRUCTURE OF A FACTOR RING R/P AND DERIVATIONS OF RKarim Bouchannafa, Lahcen Oukhtite, Moulay Abdallah Idrissi대한수학회 · 대한수학회보2023 · 제60권 제5호Some functional identities arising from derivationsAbdellah Mamouni, Lahcen Oukhtite, Mohammed Zerra대한수학회 · 대한수학회논문집2023 · 제38권 제1호On derivations and commuting like elements in prime ringsJihad Benzaid, Lahcen Oukhtite, Omar Ait Zemzami장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2024 · 제27권 제2호Central Identities in Prime Rings with Anti-Automorphisms and Generalized DerivationsAbbas Hussain Shikeh, Mohammad Aslam Siddeeque경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2025 · 제65권 제2호
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