A characterization of ordered groups by means of segments
A family of totally ordered groups with some special properties
Let be a field with a Krull valuation and value group , and let 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 should be countably generated as -modules.By [1] Prop. 1.4.1, the field is metrizable if and only if the value group has a cofinal sequence. We prove that for any fixed cardinality , there exists a metrizable field ...
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 -groups
A topological view of ordered groups
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
All subvarieties of have finite bases of identities.
Almost finite-valued -groups
An infinite collection of absolutely convex subgroups