Ore Extensions over Weakly 2-Primal Rings

Abstract

A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let $α$ be an endomorphism and $δ$ an $α$-derivation of a ring $R$. We prove that (1) If $R$ is an $(α, δ)$-compatible and weakly 2-primal ring, then $R[x; α, δ]$ is weakly semicommutative; (2) If $R$ is $(α, δ)$-compatible, then $R$ is weakly 2-primal if and only if $R[x; α, δ]$ is weakly 2-primal.