Journals Information
Mathematics and Statistics Vol. 13(4), pp. 228 - 231
DOI: 10.13189/ms.2025.130406
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Commutativity of Prime Rings with 
-generalized Derivations
Ahlam Fallatah 1, Faiza Shujat 1, Abu Zaid Ansari 2,*
1 Department of Mathematics, Faculty of Science, Taibah University, Madinah, KSA
2 Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA
ABSTRACT
An iconic example of mathematical unification is the role of derivation and their generalizations, which integrate multiple fields of study and create a useful framework for examining problems of structural importance. The fields of rings, algebra, and extended algebraic structures with derivations have seen several important revolutions in the theoretical perspective. It is a classical and long-lasting problem in the study of derivations that once a derivation that is centralizing and non-zero on a prime ring takes place, the commutative structure of the ring may exist. The current research is motivated by the study on 
-generalized derivations. Our objective is to establish the commutativity theorems by investigating some differential identities related to generalized derivations in the dense ideal of 
. We advance the techniques of how these mappings interact with the underlying algebraic structures (proper subsets of rings and extended rings) by exploring the idea of -generalized derivation. Notice that our findings give direct application to several researches in the context of generalized derivation. Considering 
and because every -generalized derivation will be the ordinary generalized derivation for 
, our results directly apply to many studies in the context of generalized derivation.
KEYWORDS
Prime Ring, Ring of Quotients, Symmetric -generalized Derivation, Centralizer
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ahlam Fallatah , Faiza Shujat , Abu Zaid Ansari , "Commutativity of Prime Rings with -generalized Derivations," Mathematics and Statistics, Vol. 13, No. 4, pp. 228 - 231, 2025. DOI: 10.13189/ms.2025.130406.
(b). APA Format:
Ahlam Fallatah , Faiza Shujat , Abu Zaid Ansari (2025). Commutativity of Prime Rings with -generalized Derivations. Mathematics and Statistics, 13(4), 228 - 231. DOI: 10.13189/ms.2025.130406.