Baer and quasi-Baer differential polynomial rings

Abstract

A ring R with a derivation is called -quasi Baer (resp. quasi-Baer), if the right annihilator of every -ideal (resp. ideal) of R is generated by an idempotent, as a right ideal. We show the left-right symmetry of -(quasi) Baer condition and prove that a ring R is -quasi Baer if and only if R[x;] is quasi Baer if and only if R[x;] is [image omitted]-quasi Baer for every extended derivation [image omitted] of . When R is a ring with IFP, then R is -Baer if and only if R[x;] is Baer if and only if R[x;] is [image omitted]-Baer for every extended derivation [image omitted] of . A rich source of examples for -(quasi) Baer rings is provided.