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Convex isomorphic ordered sets

Petr Emanovský (1993)

Mathematica Bohemica

V. I. Marmazejev introduced in [5] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered...

Convex isomorphism of Q -lattices

Petr Emanovský (1993)

Mathematica Bohemica

V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the q -lattices defined in [2] and to characterize the convex isomorphic q -lattices.

Convex isomorphisms of directed multilattices

Ján Jakubík, Mária Csontóová (1993)

Mathematica Bohemica

By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.

Convex lines in median groups

Milan Kolibiar (1992)

Archivum Mathematicum

There is proved that a convex maximal line in a median group G , containing 0, is a direct factor of G .

Convexities of lattice ordered groups

Ján Jakubík (1996)

Mathematica Bohemica

In this paper an injective mapping of the class of all infinite cardinals into the collection of all convexities of lattice ordered groups is constructed; this generalizes an earlier result on convexities of d -groups.

Convexity in subsets of lattices.

Sergei V. Ovchinnikov (1980)

Stochastica

The notion of convex set for subsets of lattices in one particular case was introduced in [1], where it was used to study Paretto's principle in the theory of group choice. This notion is based on a betweenness relation due to Glivenko [2]. Betweenness is used very widely in lattice theory as basis for lattice geometry (see [3], and, especially [4 part 1]).In the present paper the relative notions of convexity are considered for subsets of an arbitrary lattice.In section 1 certain relative notions...

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