Ore Extensions over Weakly 2-Primal Rings (Communications in Mathematical Research, 2021)
A weakly 2-primal ring is a common generalization of a semicommutativering, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Oreextensions 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 weakly2-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.
Keywords: $(α; δ)$-compatible ring; weakly 2-primal ring; weakly semicommutative ring; nil-semicommutative ring; Ore extension.