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Paper IPM / M / 749  


Abstract:  
Let C_{F}(X) denote the socle of C(X). It is shown that X is a
Pspace if and only if C(X) is ℵ_{0}selfinjective ring
or equivalently, if and only if [(C(X))/(C_{F}(X))] is
ℵ_{0}selfinjective. We also prove that X is an extremally
disconnected Pspace with only a finite number of isolated
points if and only if [(C(X))/(C_{F}(X))] is selfinjective.
Consequently, if X is a Pspace, then X is either an
extremally disconnected space with at most a countable number of
isolated points or both C(X) and [(C(X))/(C_{F}(X))] have
uncountable Goldiedimensions. Prime ideals of
[(C(X))/(C_{F}(X))] are also studied.
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