COMMUTATIVITY OF RINGS WITH SEMIDERIVATIONS

In the theory of rings, the study of commutative rings has evoked great interest and assumed importance. In particular, the study of derivations, generalized derivations, semiderivations in rings has yielded many interesting results. These results have applications in other branches of algebra. Throughout this work a ring R is a synonym for an associative ring. In this work we present some properties of associative rings, prime rings, semiprime rings, σ – prime rings which admit semideriations and Generalized semideriations; Prime rings with Left Generalized semiderivation.We prove the commutativity of rings using the semiderivations and also we use symmetric bi-derivation or permuting tri-derivation instead of derivation in definition of Jordan generalized derivation.