COMMUTATIVITY OF RINGS WITH SEMIDERIVATIONS
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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.
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