International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 9-13
doi: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 H. Al-Ezeh. 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 A〚X〛 is a PF-ring if and only if for any two countable subsets S and T of A such that S⫅annA(T), there exists c∈annA(T) such that bc=b for all b∈S. Also it is proved that a power series ring A〚X〛 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.