Weakly principally quasi-Baer skew generalized power series rings

Abstract

Let $$(S,\le )$$ be a strictly totally ordered monoid and R an $$(S,\omega )$$ -weakly rigid ring, where $$\omega :S\rightarrow End(R)$$ is a monoid homomorphism. In this paper, we study the weakly p.q.-Bear property of the skew generalized power series ring $$R[[S,\omega ]]$$ . As a consequence, the weakly p.q.-Baer property of the skew power series ring $$R[[x;\alpha ]]$$ and the skew Laurent power series ring $$R[[x,x^{-1};\alpha ]]$$ are determined, where $$\alpha$$ is a ring endomorphism of R.