Exchange PF-rings and almost PP-rings

H. Al-Ezeh

International Journal of Mathematics and Mathematical Sciences, 1989, vol. 12, 1-3

Abstract:

Let R be a commutative ring with unity. In this paper, we prove that R is an almost PP–PM–ring if and only if R is an exchange PF–ring. Let X be a completely regular Hausdorff space, and let βX be the Stone Čech compactification of X. Then we prove that the ring C(X) of all continuous real valued functions on X is an almost PP–ring if and only if X is an F–space that has an open basis of clopen sets. Finally, we deduce that the ring C(X) is an almost PP–ring if and only if C(X) is a U–ring, i.e. for each f ε C(X), there exists a unit u ε C(X) such that f = u | f | .

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:390987

DOI: 10.1155/S016117128900089X

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