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Displaying similar documents to “Contracting the socle in rings of continuous functions”

Completeness properties of function rings in pointfree topology

Bernhard Banaschewski, Sung Sa Hong (2003)

Commentationes Mathematicae Universitatis Carolinae

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This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

Archimedean frames, revisited

Jorge Martinez (2008)

Commentationes Mathematicae Universitatis Carolinae

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This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called and is . Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an element arises naturally, and the join of suitably...

Rings with zero intersection property on annihilators: Zip rings.

Carl Faith (1989)

Publicacions Matemàtiques

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Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X⊥ of a subset X of R is zero, then X1 ⊥ = 0 for a finite subset X1 ⊆ X. (ZIP 2) If L is a left ideal and if L⊥ = 0, then L1 ...