Les sous-groupes d'un groupe quasi-réticulé
Lexico extension and a cut completion of a half l-group
The cut completi on of an hl-group G with the abelian increasing part is investigated under the assumption that G is a lexico extension of its hl-subgroup.
Lexicographic extensions of dually residuated lattice ordered monoids
Dually residuated lattice ordered monoids (-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (-algebras, -algebras) and their non-commutative variants (-algebras, pseudo -algebras). In the paper, lex-extensions and lex-ideals of -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
Lexicographic factors of a linearly ordered group
Lexicographic product decompositions of a linearly ordered group
Lexicographic product decompositions of cyclically ordered groups
Lexicographic product decompositions of partially ordered quasigroups
Lexicographic products of cyclically ordered groups
Lexicographic products of half linearly ordered groups
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem...
Local analysis for semi-bounded groups
An o-minimal expansion ℳ = ⟨M,<,+,0, ...⟩ of an ordered group is called semi-bounded if it does not expand a real closed field. Possibly, it defines a real closed field with bounded domain I ⊆ M. Let us call a definable set short if it is in definable bijection with a definable subset of some Iⁿ, and long otherwise. Previous work by Edmundo and Peterzil provided structure theorems for definable sets with respect to the dichotomy ’bounded versus unbounded’. Peterzil (2009) conjectured a refined...
Locally conditioned radical classes of lattice-ordered groups
Locally finite conditions on lattice-ordered groups
Locally partially ordered groups
Locally solid topological lattice-ordered groups
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is...
L'ordre de Dehornoy sur les tresses
Maximal convergences and minimal proper convergences in -groups
Maximal Dedekind completion of a half lattice ordered group
Maximal Dedekind completion of an abelian lattice-ordered group
Measurement representations of ordered, relational structures with archimedean ordered translations
Median groups