On polynomial extensions of principally quasi-Baer rings (Q2718037)

The authors introduce right principally quasi-Baer (p.q.-Baer) rings. They prove that a ring \(R\) is a right p.q.-Baer ring if and only if the polynomial ring \(R[X]\) is a right p.q.-Baer ring. Since a PP ring is a right p.q.-Baer ring, this result generalizes the results of Armendariz and Jøndrup who have proved similar results for PP rings under the extra assumption that \(R\) is a reduced ring and a commutative ring, respectively. The authors prove that a similar result is not true for formal power series rings. Only one way is true, i.e., if \(R[[X]]\) is a right p.q.-Baer ring then so is \(R\). They produce an example to show that the reverse implication is not true.