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Rings of Continuous Functions.
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Rings of continuous functions
Contents: Functions of a Topological Space.- Ideals and Z-Filters.- Completely Regular Spaces.- Fixed Ideals. Compact Spaces.- Ordered Residue Class Rings.- The Stone-Czech Compactification.-Expand
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Concerning rings of continuous functions
The present paper deals with two distinct, though related, questions, concerning the ring C(X, R) of all continuous real-valued functions on a completely regular topological space X. The first ofExpand
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Characterization of Maximal Ideals
The promise made at the beginning of Chapter 6 that βX is to be used to characterize the maximal ideals in C(X) and in C*(X), will be fulfilled in this chapter. The key to the description of theExpand
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Some Remarks About Elementary Divisor Rings
In this and the following paper [2], we are concerned with obtaining conditions on a commutative ring S with identity element in order that every matrix over S can be reduced to an equivalentExpand
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Rings of continuous functions in which every finitely generated ideal is principal
An abstract ring in which all finitely generated ideals are principal will be called an F-ring. Let C(X) denote the ring of all continuous real-valued functions defined on a completely regularExpand
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The proof turns out to be considerably more difficult than anticipated. If we assume the continuum hypothesis (designated [CH]), then we can find such a point p (2.5); however, we do not know whetherExpand
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Rings of quotients of rings of functions
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An Isomorphism Theorem for Real-Closed Fields
A classical theorem of Steinitz [12, p. 125] states that the characteristic of an algebraically closed field, together with its absolute degree of transcendency, uniquely determine the field (up toExpand
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