Posner’s Theorem and ∗-Centralizing Derivations on Prime Ideals with Applications

A well-known result of Posner’s second theorem states that if the commutator each element in a prime ring and its image under nonzero derivation are central, then is commutative. In present paper, we extended this bluestocking to an arbitrary with involution involving ideals. Further, apart from proving several other interesting exciting results, established ∗-version Vukman’s theorem. Precisely, describe structure quotient A/L, where L ideal A. by taking advantage theorem, show 2-torsion free semiprime admits ∗-centralizing derivation, contains central ideal. This spirit classical due Bell Martindale (Theorem 3). As applications, unified theorems. Finally, conclude our paper direction for further research.