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) oF(y) = 0 for all x, y ∈ I. (ii) [d(x), F(y)] = 0 for all x, y ∈ I. (iii) d(x) o F(y) = x o y for all x, y ∈ I. (iv) d(x)F(y) − xy ∈ Z(R) forall 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 = beta on I.
@article{11384,
title = {Some generalizations in certain classes of rings with involution - doi: 10.5269/bspm.v29i1.11384},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {28},
year = {2010},
doi = {10.5269/bspm.v29i1.11384},
language = {EN},
url = {http://dml.mathdoc.fr/item/11384}
}
Huang, Shuliang. Some generalizations in certain classes of rings with involution - doi: 10.5269/bspm.v29i1.11384. Boletim da Sociedade Paranaense de Matemática, Tome 28 (2010) . doi : 10.5269/bspm.v29i1.11384. http://gdmltest.u-ga.fr/item/11384/