Identities with Multiplicative Generalized $(\alpha,\alpha)$-Derivations of Semiprime Rings
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Authors: G. S. SANDHU, A. AYRAN AND N. AYDIN
DOI: 10.46793/KgJMat2403.365S
Abstract:
Let R be a semiprime ring and α be an automorphism of R. A mapping F : R → R (not necessarily additive) is called multiplicative generalized (α,α)-derivation if there exists a unique (α,α)-derivation d of R such that F(xy) = F(x)α(y) + α(x)d(y) for all x,y ∈ R. In the present paper, we intend to study several algebraic identities involving multiplicative generalized (α,α)-derivations on appropriate subsets of semiprime rings and collect the information about the commutative structure of these rings.
Keywords:
Semiprime ring, multiplicative generalized (α,α)-derivation, (α,α)-derivation, automorphism.
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