Abstract: Let R be a ring and α be an endomorphism of R. Then, we introduce the notions of generalized reverse (α, 1)-derivation and that of symmetric generalized reverse (α, 1)-biderivation. It is shown that if a semiprime ring admits a generalized reverse (α, 1)-derivation with an associated reverse (α, 1)-derivation d, then d maps R into Z(R) and also that if a non-commutative prime ring admits a generalized reverse (α, 1)-derivation F with an associated reverse (α, 1)-derivation d, then F is reverse left α-multiplier on R. Analogous results have been proved for a symmetric generalized reverse (α, 1)-biderivation.
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Keywords and phrases: semiprime ring, prime ring, generalized reverse (α, 1)-derivation, generalized reverse (α, 1)-biderivation and symmetric generalized reverse (α, 1)-biderivation.
Received: July 22, 2022; Revised: October 4, 2022; Accepted: October 13, 2022; Published: October 22, 2022
How to cite this article: Sk. Haseena and C. Jaya Subba Reddy, Symmetric generalized reverse -biderivations in rings, JP Journal of Algebra, Number Theory and Applications 58 (2022), 37-43. http://dx.doi.org/10.17654/0972555522033
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