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Acta Mathematica Hungarica
Authors: Gary Birkenmeier, Henry Heatherly, Jin Kim, and Jae Park
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Abstract  

We extend a theorem of Kist for commutative PP rings to principally quasi-Baer rings for which every prime ideal contains a unique minimal prime ideal without using topological arguments. Also decompositions of quasi-Baer and principally quasi-Baer rings are investigated.

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A ring R is called right principally quasi-Baer (or simply right p.q.-Baer ) if the right annihilator of a principal right ideal of R is generated by an idempotent. Let R be a ring such that all left semicentral idempotents are central. Let α be an endomorphism of R which is not assumed to be surjective and R be α -compatible. It is shown that the skew power series ring R [[ x; α ]] is right p.q.-Baer if and only if the skew Laurent power series ring R [[ x, x −1 ; α ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any countable family of idempotents in R has a generalized join in I ( R ). An example showing that the α -compatible condition on R is not superfluous, is provided.

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