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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 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....

A Note on Pseudo-Kleene Algebras

Ivan Chajda (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.

A note on Stone join-semilattices

Shriram Nimbhorkar, Anwari Rahemani (2011)

Open Mathematics

Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.

A note on the symmetric difference in lattices.

Eloy Renedo, Enric Trillas, Claudio Alsina (2005)

Mathware and Soft Computing

The paper introduces a definition of symmetric difference in lattices with negation, presents its general properties and studies those that are typical of ortholattices, orthomodular lattices, De Morgan and Boolean algebras.

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