Two properties of the power series ring

H. Al-Ezeh

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-5

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 ⫅ ann A ( T ) , there exists c ∈ ann A ( T ) such that b c = 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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:192686

DOI: 10.1155/S0161171288000031

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