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Semimodularity in lower continuous strongly dually atomic lattices

Andrzej Walendziak (1996)

Archivum Mathematicum

For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].

Separation properties in congruence lattices of lattices

Miroslav Ploščica (2000)

Colloquium Mathematicae

We investigate the congruence lattices of lattices in the varieties n . Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in n have different congruence lattices.

Sequential convergences in lattices

Ján Jakubík (1992)

Mathematica Bohemica

The notion of sequential convergence on a lattice is defined in a natural way. In the present paper we investigate the system C o n v L of all sequential convergences on a lattice L .

Some characterizations of completeness for trellises in terms of joins of cycles

S. Parameshwara Bhatta, H. Shashirekha (2004)

Czechoslovak Mathematical Journal

This paper gives some new characterizations of completeness for trellises by introducing the notion of a cycle-complete trellis. One of our results yields, in particular, a characterization of completeness for trellises of finite length due to K. Gladstien (see K. Gladstien: Characterization of completeness for trellises of finite length, Algebra Universalis 3 (1973), 341–344).

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