Displaying similar documents to “Independent axiom systems for nearlattices”

Implication and equivalential reducts of basic algebras

Ivan Chajda, Miroslav Kolařík, Filip Švrček (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A term operation implication is introduced in a given basic algebra 𝒜 and properties of the implication reduct of 𝒜 are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of 𝒜 and, if this partial order is linear, the algebra 𝒜 can be reconstructed...

Lattices and semilattices having an antitone involution in every upper interval

Ivan Chajda (2003)

Commentationes Mathematicae Universitatis Carolinae

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We study ∨ -semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence properties of these varieties are investigated.