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Interval decomposition lattices are balanced

Foldes S., Radeleczki S.

Demonstratio Mathematica

2016

Vol. 49, nr 3

271--281

Intervals in binary or n-ary relations or other discrete structures generalize the concept of an interval in a linearly ordered set. They are defined abstractly as closed sets of a closure system on a set, satisfying certain axioms. Join-irreducible partitions into intervals are characterized in the lattice of all interval decompositions. This result is used to show that the lattice of interval decompositions is balanced, and the case when this lattice is distributive is also characterised.

On generating sets of finite algebras

Krempa J., Stocka A.

Demonstratio Mathematica

2015

Vol. 48, nr 4

554--561

We consider here some notions and results about sets of generators of finite algebras motivated by the case of finite groups. We illustrate these notions by simple examples closed to lattices and semigroups. Next, we examine these notions in the case of groups with operators.

Some characterizations of pseudo-BL-chains

Walendziak A., Wojciechowska-Rysiawa M.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

121-124

Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.