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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.
About the author
Author Prof. A. S. Khairnar is a professor at Department of Mathematics, MES Abasaheb Garware College, Pune. Author obtained his M.Sc. and Ph.D form Savitribai Phule Pune University. He has more than 12 research publications in various reputed journals. His research area is Algebra, Zero-divisor graph. He has co-authored 6 textbooks.
