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ON n-CENTRALIZING GENERALIZED DERIVATIONS IN SEMIPRIME RINGS WITH APPLICATIONS TO C*-ALGEBRAS

BASUDEB DHARA

Department of Mathematics, Belda College, Belda, Paschim Medinipur-721424, India

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and

SHAKIR ALI

http://www.amu.ac.in Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

Corresponding author.

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https://doi.org/10.1142/S0219498812501113Cited by:18 (Source: Crossref)

Abstract

Let R be a ring with center Z(R) and n be a fixed positive integer. A mapping f : R → R is said to be n-centralizing on a subset S of R if f(x)xⁿ – xⁿ f(x) ∈ Z(R) holds for all x ∈ S. The main result of this paper states that every n-centralizing generalized derivation F on a (n + 1)!-torsion free semiprime ring is n-commuting. Further, we prove that if a generalized derivation F : R → R is n-centralizing on a nonzero left ideal λ, then either R contains a nonzero central ideal or λD(Z) ⊆ Z(R) for some derivation D of R. As an application, n-centralizing generalized derivations of C*-algebras are characterized.

Keywords:

AMSC: 16W25, 16R50, 16N60

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