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Displaying similar documents to “Congruence kernels of orthoimplication algebras.”

Separation properties in congruence lattices of lattices

Miroslav Ploščica (2000)

Colloquium Mathematicae

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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.

Relatively pseudocomplemented directoids

Ivan Chajda (2009)

Commentationes Mathematicae Universitatis Carolinae

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The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called p -ideals.

Discriminator varieties of Boolean algebras with residuated operators

Peter Jipsen (1993)

Banach Center Publications

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The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative...