∇-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, $\ast$-(semi)prime ideal, (semi)prime ring and $\ast$-(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.

Keywords:

• Derivation
• prime ring
• ∇-prime ring
• automorphism
• involution
• anti-automorphism

AMS Subject classification 2020:

• 16N60
• 16W10
• 16W25
• 16W20

Disclosure statement

No potential conflict of interest was reported by the author(s).