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On C(X) Modulo its socle
by
O.A.S. Karamzadeh
Chamran University, Ahvaz, Iran
Coauthors: A.E. Estaji
Let C_F(X) denote the socle of C(X). It is shown that X is a P-space if and only if C(X) is an aleph_0-self-injective ring or equivalently, if and only if C(X)/C_F(X) is aleph_0-self-injective. We also prove that X is an extremely disconnected P-space with only a finite number of isolated points if and only if C(X)/C_F(X) is self-injective. Consequently, if X is a P-space, then X is either an extremely disconnected space with at most a countable number of isolated points or both C(X) and C(X)/C_F(X) have uncountable Goldie dimension. Prime ideals of C(X)/C_F(X) are also studied
Date received: June 6, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagx-13.