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$S V$ -Rings and $S V$ -Porings

Niels Schwartz (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

$S V$ -rings are commutative rings whose factor rings modulo prime ideals are valuation rings. $S V$ -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of $S V$ -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered $S V$ -rings ( $S V$ -porings) are introduced, and...

Sacks forcing collapses $𝔠$ to $𝔟$

Petr Simon (1993)

Commentationes Mathematicae Universitatis Carolinae

We shall prove that Sacks algebra is nowhere $(𝔟, 𝔠, 𝔠)$ -distributive, which implies that Sacks forcing collapses $𝔠$ to $𝔟$ .

Samuel compactification and uniform coreflection of nearness $σ$ -frames

Inderasan Naidoo (2006)

Czechoslovak Mathematical Journal

We introduce the structure of a nearness on a $σ$ -frame and construct the coreflection of the category $𝐍 σ F r m$ of nearness $σ$ -frames to the category $𝐊 R e g σ F r m$ of compact regular $σ$ -frames. This description of the Samuel compactification of a nearness $σ$ -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform $σ$ -frames in [11]. We also construct the uniform coreflection of a nearness $σ$ -frame, that is, the coreflection of the category of $𝐍 σ F r m$ to the category...

Sandwich sets and partial order.

R.J. Koch (1984)

Semigroup forum

Saturated Boolean Algebras With Ultrafilters

Žarko Mijajlović (1979)

Publications de l'Institut Mathématique

Saturated Boolean algebras with ultrafilters.

Z. Mijajlovic (1979)

Publications de l'Institut Mathématique [Elektronische Ressource]

Schwache Teilbarkeitshalbgruppen.

B. Bosbach (1976)

Semigroup forum

Selfduality of the system of convex subsets of a partially ordered set

Miron Zelina (1993)

Commentationes Mathematicae Universitatis Carolinae

For a partially ordered set $P$ let us denote by $C o P$ the system of all convex subsets of $P$ . It is found the necessary and sufficient condition (concerning $P$ ) under which $C o P$ (as a partially ordered set) is selfdual.