On ⁎-strong Commutativity Preserving with Endomorphisms

Abstract

In this paper, we investigate commutativity of a prime ring with involution. More specifically, we introduce certain algebraic identities of ∗-strong commutativity with two endomorphisms, and study their connection with the commutativity of these rings. Finally, we provide examples to show that the various restrictions imposed in the hypothesis of our theorems are necessary.

Key words and phrases. Prime ring, involution, commutativity, endomorphism.

2010 Mathematics Subject Classification. 16N60, 16W10, 16W25