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- W2182155287 abstract "The essentiality of prime ideals and z-ideals of C(X) modulo the socle and principal ideals of C(X) are investigated. We show that the Goldie dimension of C(X) modulo its socle is greater than or equal to that of C(X) and the equality may not always hold. Topological spaces X for which the Jacobson radical of C(X) modulo its socle is zero are characterized. Using this characterization, it turns out that for a compact space X, the Jacobson radical of C(X) modulo its socle is zero if and only if the set of isolated points of C(X) is finite." @default.
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- W2182155287 date "2000-01-01" @default.
- W2182155287 modified "2023-10-03" @default.
- W2182155287 title "The ring C(X) modulo its socle and principal ideals" @default.
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