A characterization of ordered groups by means of segments
A common abstraction of boolean rings and lattice ordered groups
A directed -group that is not a group of divisibility
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 non commutative generalization of -autonomous lattices
Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
A non-commutative generalization of -algebras
A note on homogeneous lattices
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.
A weakly associative generalization of the variety of representable lattice ordered groups
Abgeschlossene vollständige -Untergruppen der Verbandsgruppen
About varieties of weakly abelian -groups
Affine completeness and wreath product decompositions of lattice ordered group
Let and be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of and fails to be affine complete.
Affine completeness of complete lattice ordered groups
Affine completness of projectable lattice ordered groups
Algebraic and categorical properties of -ideal systems.
All subvarieties of have finite bases of identities.
Almost finite-valued -groups
An infinite collection of absolutely convex subgroups