Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2016.56.2.343
Title & Authors
Posner`s First Theorem for *-ideals in Prime Rings with Involution Ashraf, Mohammad; Siddeeque, Mohammad Aslam;
Posner`s first theorem states that if R is a prime ring of characteristic different from two, and are derivations on R such that the iterate is also a derivation of R, then at least one of , is zero. In the present paper we extend this result to *-prime rings of characteristic different from two.
Rings with involution;derivation;*-prime ring and *-ideal;
M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra, 156(1993), 385-394.
I. N. Herstein, Rings with involution, The University of Chicago Press, Chicago, (1976).
I. N. Herstein, A note on derivations, Canad. Math. Bull., 21(1978), 369-370.
M. Mathieu, Posner's second theorem deduced from the first, Proc. Amer. Math. Soc., 114(1992), 601-602.
L. Oukhtite, Posner's second theorem for jordan ideals in rings with involution, Expositiones Mathematicae, 29(2011), 415-419.
L. Oukhtite and S. Salhi, On commutativity of *-prime rings, Glasnik Matematicki, 41(2006), no.1, 57-64.
L. Oukhtite and S. Salhi, Derivations and commutativity of *-prime rings, Int. J. Contemp. Math. Sci., 1(9)(2006), 439-448.
E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8(1957), 1093-1100.