A note on the symmetric difference in lattices.

Eloy Renedo; Enric Trillas; Claudio Alsina

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Orthomodular Lattices

Elżbieta Mądra, Adam Grabowski (2008)

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The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.As a preliminary work, we present the proofs of the dependence...

On the one class of hyperbolic systems.

Adler, Vsevolod E., Shabat, Alexey B. (2006)

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On the variety Csub $(D)$

Václav Slavík (1991)

Commentationes Mathematicae Universitatis Carolinae

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The variety of lattices generated by lattices of all convex sublattices of distributive lattices is investigated.

Separation properties in congruence lattices of lattices

Miroslav Ploščica (2000)

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We investigate the congruence lattices of lattices in the varieties $ℳ_{n}$ . 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 $ℳ_{n}$ have different congruence lattices.

On direct decompositions of certain orthomodular lattices.

Konôpka, P., Pulmannová, S. (1991)

Acta Mathematica Universitatis Comenianae. New Series

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The Nikodym property and local properties of Boolean algebras

Antonio Aizpuru (1996)

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We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.

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G. Grätzer, A. Kisielewicz, B. Wolk (1992)

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Program Algebra over an Algebra

Grzegorz Bancerek (2012)

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We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms. ...