Skew Hurwitz serieswise quasi-armendariz rings

For a ring endomorphism [Formula: see text], a generalization of semiprime rings and right p.q.-Baer rings, which we call quasi-Armendariz rings of skew Hurwitz series type (or simply, [Formula: see text]-[Formula: see text]), is introduced and studied. It is shown that the [Formula: see text]-rings are closed upper triangular matrix rings, full matrix rings and Morita invariance. Some characterizations for the skew Hurwitz series ring [Formula: see text] to be quasi-Baer, generalized quasi-Baer, primary, nilary, reflexive, ideal-symmetric and semiprime are concluded.

On skew Hurwitz serieswise Armendariz rings

For a ring endomorphism α, we introduce and investigate skew Hurwitz serieswise Armendariz (or SHA) rings which are a generalization of α-rigid rings and determine the radicals of the skew Hurwitz series ring (HR, α), in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SHA-ring. We also construct various types of nonreduced SHA-rings.