FUNCTIONAL IDENTITIES ON SEMIPRIME RINGS WITH MULTIPLICATIVE (GENERALIZED)-DERIVATIONS

Abstract

The main purpose of this project was to study some functional identities on semiprime rings with multiplicative (generalized)-derivations. This is because, which facilitate semiprime ring is essential in multiplicative (generalized)-derivation. The important preliminary concepts, examples, lemmas and theorems were presented to make the concept of functional identities on semiprime rings with multiplicative (generalized)-derivations more clear. In order to study functional identities on semiprime rings with multiplicative (generalized)-derivations used many methods such as commuting map, derivation, multiplicative derivation, left ideal, multiplicative left centralizer and multiplicative (generalized)-derivation were presented. The results show that semiprime ring is essential in all theorems and multiplicative (generalized)derivations is commuting map on left ideal Finally, results of some examples shows that essentiality semiprimeness.