Weakly p.q.-Baer skew Hurwitz series rings

Abstract

A ring [Formula: see text] is projective invariant Baer ([Formula: see text]-Baer for short) if the right annihilator of every projection invariant left ideal of [Formula: see text] is generated by an idempotent element of [Formula: see text]. A ring [Formula: see text] is called weakly principally quasi-Baer or simply (weakly p.q.-Baer) if the right annihilator of a principal right ideal is left [Formula: see text]-unital by left semicentral idempotents, which implies that [Formula: see text] modulo, the right annihilator of any principal right ideal, is flat. We study relations between the [Formula: see text]-Baer and weakly p.q.-Baer properties of a ring [Formula: see text], and its skew Hurwitz series ring [Formula: see text], where [Formula: see text] is a ring equipped with an endomorphism [Formula: see text]. Examples are provided to explain the results.