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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...

Semilattices with sectional mappings

Ivan Chajda, Günther Eigenthaler (2007)

Discussiones Mathematicae - General Algebra and Applications

We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].

Semi-ordered groups

Jiří Rachůnek (1979)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

Sequential convergences on free lattice ordered groups

Ján Jakubík (1992)

Mathematica Bohemica

In this paper the partially ordered set Conv G of all sequential convergences on G is investigated, where G is either a free lattice ordered group or a free abelian lattice ordered group.

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