A Note on Homomorphisms and Anti-Homomorphisms on ∗-Ring

Nadeem ur Rehman, Abu Zaid Ansari, Claus Haetinger

Abstract

In this paper we describe generalized left $\ast$-derivation $F:R\to R$ in
$\ast$-prime ring and prove that if $F$ acts as homomorphism or anti-homomorphism on $R$, then either $R$ is commutative or $F$ is a right $\ast$-centralizer on $R$. Analogous results have been proved for generalized left $\ast$-biderivation and Jordan $\ast$-centralizer on $R$.