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Some generalizations in certain classes of rings with involution

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Author(s): Shuliang Huang

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 29;
Issue: 1;
Start page: 9;
Date: 2011;
Original page

Keywords: sigma-prime ring | derivation | generalized derivation | (alpha | beta )-derivation | commutativity.

ABSTRACT
Let R be a 2-torsion free sigma-prime ring with an involution sigma, I a nonzero sigma-ideal of R. In this paper we explore the commutativity of R satisfying any one of the properties: (i)d(x)◦F(y) = 0 for all x, y ∈ I. (ii) [d(x),F(y)] = 0 for all x,y ∈ I. (iii) d(x)◦F(y) = x◦y for all x, y ∈ I. (iv) d(x)F(y) − xy ∈ Z(R) for all x, y ∈ I. We also discuss (alpha,beta)-derivations of sigma-prime rings and prove that if G is an (alpha,beta)-derivation which acts as a homomorphism or as an anti-homomorphism on I, then G = 0 or G = on I.
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