ON GENERALIZED (α, β)-DERIVATIONS AND COMMUTATIVITY IN PRIME RINGS

Title & Authors
ON GENERALIZED (α, β)-DERIVATIONS AND COMMUTATIVITY IN PRIME RINGS
Jung, Yong-Soo; Park, Kyoo-Hong;

Abstract
Let R be a prime ring and I a nonzero ideal of R. Let $\small{\alpha,\;\nu,\;\tau\;R{\rightarrow}R}$ be the endomorphisms and $\small{\beta,\;\mu\;R{\rightarrow}R}$ the automorphisms. If R admits a generalized $\small{(\alpha,\;\beta)-derivation}$ g associated with a nonzero $\small{(\alpha,\;\beta)-derivation\;\delta}$ such that $\small{g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau}$ for all x, y $\small{{\in}I}$, then R is commutative.
Keywords
generalized $\small{(\alpha,\;\beta)-derivation}$;prime ring;commutativity;
Language
English
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1.
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2.
On Generalized ()-Derivations in Semiprime Rings, ISRN Algebra, 2012, 2012, 1
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