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http://dx.doi.org/10.5666/KMJ.2021.61.4.727

Identities in a Prime Ideal of a Ring Involving Generalized Derivations  

ur Rehman, Nadeem (Department of Mathematics, Aligarh Muslim University)
Ali Alnoghashi, Hafedh Mohsen (Department of Mathematics, Aligarh Muslim University)
Boua, Abdelkarim (Polydisciplinary Faculty, LSI, Taza, Sidi Mohammed Ben Abdellah University Fez)
Publication Information
Kyungpook Mathematical Journal / v.61, no.4, 2021 , pp. 727-735 More about this Journal
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.
Keywords
Prime ideal; generalized derivations; commutativity;
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1 L. K. Ardakani, B. Davvaz and S. Huang, On derivations of prime and semi-prime Gamma rings, Bol. Soc. Param. Mat., 37(2)(2019), 155-164.
2 H. E. Bell and L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta. Math. Hungar., 53(1989), 339-346.   DOI
3 A. Mamouni, L. Oukhtite and M. Zerra, On derivations involving prime ideals and commutativity in rings, Sao Paulo J. Math. Sci., 14(2020), 675-688.   DOI
4 H. E. Mir, A. Mamouni and L. Oukhtite, Commutativity with algebraic identities involving prime ideals, Commun. Korean Math. Soc., 35(3)(2020), 723-731.   DOI
5 N. Rehman, On generalized derivations as homomorphisms and anti-homomorphisms, Glas. Mat., 39(59)(2004), 27-30.   DOI
6 N. Rehman, F. Alsarari and H. AlNoghashi, Action of prime ideals on generalized derivations-I, Preprint.
7 G. S. Sandhu and B. Davvaz, On generalized derivations and Jordan ideals of prime rings, Rend. Circ. Mat. Palermo, II Ser., (2020), https://doi.org/10.1007/s12215-020-00492-8.   DOI
8 B. Davvaz and M. A. Raza, A note on automorphisms of Lie ideals in prime rings, Math. Slovaca, 68(5)(2018), 1223-1229.   DOI