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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 1, Pages 9-13
http://dx.doi.org/10.1155/S0161171288000031

Two properties of the power series ring

Department of Mathematics, University of Jordan, Amman, Jordan

Received 31 July 1986; Revised 29 October 1986

Copyright © 1988 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, A, it is proved that the power series ring AX is a PF-ring if and only if for any two countable subsets S and T of A such that SannA(T), there exists cannA(T) such that bc=b for all bS. Also it is proved that a power series ring AX is a PP-ring if and only if A is a PP-ring in which every increasing chain of idempotents in A has a supremum which is an idempotent.