JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

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CHARACTERIZING IDENTITIES WITH GENERALIZED SKEW-DERIVATIONS ON PRIME IDEALS

Authors

  • G. Naga Malleswari
  • G. Swapna
  • S. Sreenivasulu

Keywords:

Integral domain, derivation, Prime ideal, Generalized derivations.

DOI:

https://doi.org/10.17654/0972555525036

Abstract

This work focuses on examining commutativity of a quotient ring $\mathrm{P} / \Pi$, where P is a ring and $\Pi$ is a prime ideal of P that allows multiplicative generalized skew-derivations satisfying certain algebraic identities imposed on prime ideals $\Pi$.

Received: February 4, 2025
Revised: September 2, 2025
Accepted: September 4, 2025

References

[1] E. C. Posner, Derivations on prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093 1100.

[2] I. N. Herstein, A note on derivations. II, Canad. Math. Bull. 22 (1979), 509-511.

[3] M. N. Daif and H. E. Bell, Remarks on derivations on semiprime rings, Int. J. Math. Math. Sci. 15 (1992), 205-206.

[4] G. N. Malleswari, S. Sreenivasulu and G. Shobhalatha, Semiprime rings with multiplicative (generalized)-derivations involving left multipliers, Creat. Math. Inform. 30(1) (2021), 61-68.

[5] Hajar El Mir, Abdellah Mamouni and Lahcen Oukhtite, Commutativity with algebraic identities involving prime ideals, Commun. Korean Math. Soc. 35(3) (2020), 723-731.

[6] A. Mamouni, L. Oukhtite and M. Zerra, On derivations involving prime ideals and commutativity in rings, São Paulo Journal of Mathematical Sciences 14 (2020), 675-688.

[7] Vincenzo De Filippis and Onofrio Mario Di Vincenzo, Generalized skew derivations on semiprime rings, Linear Multilinear Algebra 63 (2015), 927 939.

[8] S. K. Tiwari, R. K. Sharma and B. Dhara, Some theorems of commutativity of semiprime rings with mappings, Southeast Asian Bull. Math. 42 (2018), 279-292.

[9] L. Carini, V. De Filippis and G. Scudo, Identities with product of generalized skew derivations on multilinear polynomials, Comm. Algebra 44 (2016), 3122-3138.

[10] L. Carini, V. De Filippis and F. Wei, Generalized skew derivations co-centralizing multilinear polynomials, Mediterr. J. Math. 13 (2016), 2397-2424.

[11] G. S. Sandhu, A. Ayran and N. Aydin, Identities with multiplicative generalized -derivation of semiprime rings, Kragujevac J. Math. 48(3) (2021), 365-382.

[12] G. N. Malleswari, S. Sreenivasulu and G. Shobhalatha, Some identities involving multiplicative (generalized) -derivations in semiprime rings, J. Indones. Math. Soc. 28(1) (2022), 44-51.

[13] W. Ahmed and M. R. Mozumder, Multiplicative generalized skew-derivations on ideals in semiprime rings, Palest. J. Math. 13(1) (2024), 242 251.

[14] N. Rehman, F. Alsarari and H. Alnoghashi, Action of prime ideals on generalized derivations-I, 2021. arXiv: 2107.06769.

https://dx.doi.org/10.48550/arXiv.2107.06769.

Published

2025-09-26

Issue

Section

Articles

How to Cite

CHARACTERIZING IDENTITIES WITH GENERALIZED SKEW-DERIVATIONS ON PRIME IDEALS. (2025). JP Journal of Algebra, Number Theory and Applications, 64(6), 685-695. https://doi.org/10.17654/0972555525036

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