Extensions of Baer P.P. Rings and Modules

Kaplansky introduced the concept of a Baer ring a ring in which right annihilator of every non empty subset is a right ideal generated by an idempotent. A p.p. ring is a generalization of a Baer ring. A ring R is called a right p.p. ring if right annihilator of every element of R is a right ideal generated by an idempotent in R. A ring R is called a p.s. ring if right annihilator of any maximal ideal of R is a right ideal generated by an idempotent in R. In this book we present the results about extensions of p.s. property of a ring R to the polynomial ring R[x] and the power series ring R[[x]]. We also study extensions of Baer p.q. Baer and p.p. modules to polynomial power series Laurent polynomial and Laurent power series modules.