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Displaying 1 – 20 of 139

A characterization of ordered groups by means of segments

Jiří Rachůnek (1982)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

A family of totally ordered groups with some special properties

Elena Olivos (2005)

Annales mathématiques Blaise Pascal

Let $K$ be a field with a Krull valuation $| |$ and value group $G \neq {1}$ , and let $B_{K}$ be the valuation ring. Theories about spaces of countable type and Hilbert-like spaces in [1] and spaces of continuous linear operators in [2] require that all absolutely convex subsets of the base field $K$ should be countably generated as $B_{K}$ -modules.By [1] Prop. 1.4.1, the field $K$ is metrizable if and only if the value group $G$ has a cofinal sequence. We prove that for any fixed cardinality $ℵ_{κ}$ , there exists a metrizable field $K$ ...

A remark on radical-semisimple classes of fully ordered groups

Stefan Veldsman (1987)

Commentationes Mathematicae Universitatis Carolinae

A simple proof of Vinogradov’s theorem on the orderability of the free product of $o$ -groups

Gábor Révész (1987)

Czechoslovak Mathematical Journal

A topological view of ordered groups

Dale Rolfsen (2014)

Banach Center Publications

In this expository article we use topological ideas, notably compactness, to establish certain basic properties of orderable groups. Many of the properties we shall discuss are well-known, but I believe some of the proofs are new. These will be used, in turn, to prove some orderability results, including the left-orderability of the group of PL homeomorphisms of a surface with boundary, which are fixed on at least one boundary component.

Affine completeness of complete lattice ordered groups

Ján Jakubík (1995)

Czechoslovak Mathematical Journal

All subvarieties of $ℒ_{p q}$ have finite bases of identities.

Naritsyn, N. N. (2003)

Sibirskij Matematicheskij Zhurnal

Almost finite-valued $l$ -groups

Jorge Martinez (1982)

Rendiconti del Seminario Matematico della Università di Padova

An infinite collection of absolutely convex subgroups

Herbert A. Hollister (1992)

Czechoslovak Mathematical Journal

Bases of minimal elements of some partially ordered free abelian groups

Pavel Příhoda (2003)

Commentationes Mathematicae Universitatis Carolinae

In the present paper, we will show that the set of minimal elements of a full affine semigroup $A ↪ ℕ_{0}^{k}$ contains a free basis of the group generated by $A$ in $ℤ^{k}$ . This will be applied to the study of the group $K_{0} (R)$ for a semilocal ring $R$ .

Cantor extension of a half lineary cyclically ordered group

Štefan Černák (2001)

Discussiones Mathematicae - General Algebra and Applications

Convergent and fundamental sequences are studied in a half linearly cyclically ordered group G with the abelian increasing part. The main result is the construction of the Cantor extension of G.

There is proved that a convex maximal line in a median group $G$ , containing 0, is a direct factor of $G$ .

Currently displaying 1 – 20 of 139

Page 1 Next

Displaying 1 – 20 of 139

A characterization of ordered groups by means of segments

A family of totally ordered groups with some special properties

A remark on radical-semisimple classes of fully ordered groups

A simple proof of Vinogradov’s theorem on the orderability of the free product of $o$ -groups

A topological view of ordered groups

Affine completeness of complete lattice ordered groups

All subvarieties of $ℒ_{p q}$ have finite bases of identities.

Almost finite-valued $l$ -groups

An infinite collection of absolutely convex subgroups

Bases of minimal elements of some partially ordered free abelian groups

Cantor extension of a half lineary cyclically ordered group

Closure operators on radical classes of lattice-ordered groups

Compatible elements in partly ordered groups.

Completion of a cyclically ordered group

Completions of lattice ordered groups

Convergence with a fixed regulator in Archimedean lattice ordered groups

Convex lines in median groups

Coverings in the lattice of quasivarieties of $ℓ$ -groups.

Cyclic extensions of the Medvedev ordered groups

Direct limits of cyclically ordered groups

Currently displaying 1 – 20 of 139