Displaying similar documents to “Convex isomorphic ordered sets”

Pseudocomplemented ordered sets

Radomír Halaš (1993)

Archivum Mathematicum

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The aim of this paper is to transfer the concept of pseudocomplement from lattices to ordered sets and to prove some basic results holding for pseudocomplemented ordered sets.

Distributive ordered sets and relative pseudocomplements

Josef Niederle (2006)

Discussiones Mathematicae - General Algebra and Applications

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Brouwerian ordered sets generalize Brouwerian lattices. The aim of this paper is to characterize (α)-complete Brouwerian ordered sets in a manner similar to that used previously for pseudocomplemented, Stone, Boolean and distributive ordered sets. The sublattice (G(P)) in the Dedekind-Mac~Neille completion (DM(P)) of an ordered set (P) generated by (P) is said to be the characteristic lattice of (P). We can define a stronger notion of Brouwerianicity by demanding that both (P) and (G(P))...

Relatively complemented ordered sets

Ivan Chajda, Zuzana Morávková (2000)

Discussiones Mathematicae - General Algebra and Applications

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We investigate conditions for the existence of relative complements in ordered sets. For relatively complemented ordered sets with 0 we show that each element b ≠ 0 is the least one of the set of all upper bounds of all atoms contained in b.

Convex isomorphism of Q -lattices

Petr Emanovský (1993)

Mathematica Bohemica

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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.