(U, M) -derivations in prime ?-rings

Abstract

In this article, we define (U,M)-derivation d of a ? -ring M . For a Lie ideal U of a 2 - torsion free prime ? -ring M satisfying the condition a?b?c = a?b?c for all a,b, c?M and ? ,? ?? , we prove the following results:

(i) ifU is an admissible Lie ideal of M, then d(u?v) = d(u)?v + u?d(v) for all u, v?U ,? ??

(ii) if u?u?U for all u?U,? ?? , then d(u?m) = d(u)?m + u?d(m) for all m ? M

Bangladesh J. Sci. Res. 27(2): 143-153, December-2014