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A note on Boolean algebras

Isaac Gorelic (1994)

Commentationes Mathematicae Universitatis Carolinae

We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.

A note on congruence systems of MS-algebras

M. Campercholi, Diego Vaggione (2007)

Mathematica Bohemica

Let L be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences ( θ 1 , ... , θ n ; x 1 , ... , x n ) in L can be reduced to solving the restriction of the system to the skeleton of L , plus solving the restrictions of the system to the intervals [ x 1 , x ¯ ¯ 1 ] , , [ x n , x ¯ ¯ n ] .

A note on convex sublattices of lattices

Václav Slavík (1995)

Commentationes Mathematicae Universitatis Carolinae

Let C S u b ( K ) denote the variety of lattices generated by convex sublattices of lattices in K . For any proper variety V , the variety C S u b ( V ) is proper. There are uncountably many varieties V with C S u b ( V ) = V .

A note on cylindric lattices

Ivo Düntsch (1993)

Banach Center Publications

0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further research....

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