(untitled) (Communications in Mathematical Research, 2021)
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.