Ore Extensions of Quasi-Baer Rings

We first study the quasi-Baerness of Rx; σ, δ] over a quasi-Baer ring R when σ is an automorphism of R, obtaining an affirmative result. We next show that if R is a right principally quasi-Baer ring and σ is an automorphism of R with σ(e) = e for any left semicentral idempotent e ∈ R, then Rx; σ, δ] is right principally quasi-Baer. As a corollary, we have that Rx; δ] over a right principally quasi-Baer ring R is right principally quasi-Baer. Finally, we give conditions under which the quasi-Baernesses (right principal quasi-Baernesses) of R and Rx; σ, δ] are equivalent.