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Exchange PF-rings and almost PP-rings

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  • H. Al-Ezeh

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 | .

Suggested Citation

  • H. Al-Ezeh, 1989. "Exchange PF-rings and almost PP-rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:390987
    DOI: 10.1155/S016117128900089X
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