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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 orderings

Vítězslav Novák, Miroslav Novotný (2000)

Czechoslovak Mathematical Journal

A construction is given which makes it possible to find all linear extensions of a given ordered set and, conversely, to find all orderings on a given set with a prescribed linear extension. Further, dense subsets of ordered sets are studied and a procedure is presented which extends a linear extension constructed on a dense subset to the whole set.

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...

Linear operators preserving maximal column ranks of nonbinary boolean matrices

Seok-Zun Song, Sung-Dae Yang, Sung-Min Hong, Young-Bae Jun, Seon-Jeong Kim (2000)

Discussiones Mathematicae - General Algebra and Applications

The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.

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.

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