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International Journal of Mathematics and Mathematical Sciences
Volume 10, Issue 2, Pages 311-314
http://dx.doi.org/10.1155/S0161171287000371

On some properties of polynomials rings

Department of Mathematics, University of Jordan, Amman, Jordan

Received 4 February 1986; Revised 29 April 1986

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, annR(a), for each a ϵ R is a pure ideal in R, Also it is proved that the polynomial ring, R[X], is a PF-ring if and only if R is a PF-ring. Finally, we prove that R is a PP-ring if and only if R[X] is a PP-ring.