%0 Journal Article
%T Some generalizations in certain classes of rings with involution
%A Shuliang Huang
%J Boletim da Sociedade Paranaense de Matem│tica
%D 2011
%I Sociedade Brasileira de Matem│tica
%X 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.
%K sigma-prime ring
%K derivation
%K generalized derivation
%K (alpha
%K beta )-derivation
%K commutativity.
%U http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11384/6171