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• W2064351613 abstract "It is observed that X is an F-space if and only if C(X) is locally a domain (i.e., C(X)P is a domain for each prime ideal P of C(X)). Consequently, X is an F-space if and only if the primary ideals of C(X) in any given maximal ideal in C(X) are comparable. Some of the properties of C(X), where X is an F-space, are extended to general reduced Bézout rings. It is observed that whenever X is an infinite connected F-space, then C(X) is a natural example of a non-Noetherian ring without nontrivial idempotents which is locally a domain but not a domain. We observe that the rank of a point x ∈ βX, in case finite, coincides with the Goldie dimension of C(X)Mx and give an example to show that the Goldie dimension of C(X)Mx is not necessarily equal to the cardinality of the set of minimal prime ideals in Mx. Motivated by these facts and some other appropriate ones, we define the rank of a point x ∈ βX to be the Goldie dimension of C(X)Mx. Finally, for each cardinal a, we show that there exists a space X and a multiplicatively closed set S in C(X) such that the Goldie dimension of S–1 C(X) is a." @default.
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• W2064351613 date "2015-01-02" @default.
• W2064351613 modified "2023-10-03" @default.
• W2064351613 title "Goldie dimension of rings of fractions of<i>C</i>(<i>X</i>)" @default.
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• W2064351613 doi "https://doi.org/10.2989/16073606.2014.923189" @default.
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