“School of Mathematics”
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| Paper IPM / M / 749 |
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| Abstract: | |||||
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Let CF(X) denote the socle of C(X). It is shown that X is a
P-space if and only if C(X) is ℵ0-selfinjective ring
or equivalently, if and only if [(C(X))/(CF(X))] is
ℵ0-selfinjective. We also prove that X is an extremally
disconnected P-space with only a finite number of isolated
points if and only if [(C(X))/(CF(X))] is selfinjective.
Consequently, if X is a P-space, then X is either an
extremally disconnected space with at most a countable number of
isolated points or both C(X) and [(C(X))/(CF(X))] have
uncountable Goldie-dimensions. Prime ideals of
[(C(X))/(CF(X))] are also studied.
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