∇-prime rings and their commutativity

Abstract

Consider a ring with an (anti)-automorphism ∇ of finite order. The fundamental aim of this manuscript is to introduce the notions of ∇-(semi)prime ideal and ∇-(semi)prime ring as a generalization of the notions of (semi)prime ideal, ∗ -(semi)prime ideal, (semi)prime ring and ∗ -(semi)prime ring. Furthermore, we will investigate their basic properties and study the commutative property of ∇-prime rings which satisfy certain central differential identities on ∇-ideals.