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Lexico extension and a cut completion of a half l-group

Štefan Černák, Milan Demko (2002)

Discussiones Mathematicae - General Algebra and Applications

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

Jiří Rachůnek, Dana Šalounová (2004)

Mathematica Bohemica

Dually residuated lattice ordered monoids ( D R ℓ -monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ( M V -algebras, B L -algebras) and their non-commutative variants ( G M V -algebras, pseudo B L -algebras). In the paper, lex-extensions and lex-ideals of D R ℓ -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.

Lexicographic product decompositions of half linearly ordered loops

Milan Demko (2007)

Czechoslovak Mathematical Journal

In this paper we prove for an hl-loop Q 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 Q with a finite number of lexicographic factors have isomorphic refinements.

Lexicographic products of half linearly ordered groups

Ján Jakubík (2001)

Czechoslovak Mathematical Journal

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...

Linear extensions of orders invariant under abelian group actions

Alexander R. Pruss (2014)

Colloquium Mathematicae

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...

Local analysis for semi-bounded groups

Pantelis E. Eleftheriou (2012)

Fundamenta Mathematicae

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 ℓ -monoids

Jiří Rachůnek, Dana Šalounová (2007)

Czechoslovak Mathematical Journal

Bounded commutative residuated lattice ordered monoids ( R ℓ -monoids) are a common generalization of, e.g., B L -algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative R ℓ -monoids are investigated.

Local/global uniform approximation of real-valued continuous functions

Anthony W. Hager (2011)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space X , C ( X ) is the lattice-ordered group ( l -group) of real-valued continuous functions on X , and C * ( X ) is the sub- l -group of bounded functions. A property that X might have is (AP) whenever G is a divisible sub- l -group of C * ( X ) , containing the constant function 1, and separating points from closed sets in X , then any function in C ( X ) can be approximated uniformly over X by functions which are locally in G . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...

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