Le théorème de Jordan-Hölder dans certains groupoïdes ordonnés
Left translations of compact semilattices and generalizations
Les cônes autopolaires en dimension finie
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 half linearly ordered loops
In this paper we prove for an hl-loop an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop with a finite number of lexicographic factors have isomorphic refinements.
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...
Lex-ideals of DR-monoids and GMV-algebras
Linear extensions of orders invariant under abelian group actions
Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B...
Lineare Erweiterungen der teilweisen Anordnung in Ringen
Linearly fundamentally ordered semigroups
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...
Local bounded commutative residuated -monoids
Bounded commutative residuated lattice ordered monoids (-monoids) are a common generalization of, e.g., -algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative -monoids are investigated.
Local convexity in topological lattices