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Implication algebras

Ivan Chajda (2006)

Discussiones Mathematicae - General Algebra and Applications

We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....

Implication and equivalential reducts of basic algebras

Ivan Chajda, Miroslav Kolařík, Filip Švrček (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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 by means of...

Incidence structures of type ( p , n )

František Machala (2003)

Czechoslovak Mathematical Journal

Every incidence structure 𝒥 (understood as a triple of sets ( G , M , I ) , I ⊆ G × M ) admits for every positive integer p an incidence structure 𝒥 p = ( G p , M p , I p ) where G p ( M p ) consists of all independent p -element subsets in G ( M ) and I p is determined by some bijections. In the paper such incidence structures 𝒥 are investigated the 𝒥 p ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets G and M .

Infinite algebras with 3-transitive groups of weak automorphisms

László Szabó (2001)

Archivum Mathematicum

The infinite algebras with 3-transitive groups of weak automorphisms are investigated. Among others it is shown that if an infinite algebra with 3-transitive group of weak automorphisms has a nontrivial idempotent polynomial operation then either it is locally functionally complete or it is polynomially equivalent to a vector space over the two element field or it is a simple algebra that is semi-affine with respect to an elementary 2-group. In the second and third cases the group of weak automorphisms...

Intervals in partial monounary algebras

Danica Jakubíková-Studenovská (1991)

Mathematica Bohemica

In this paper the notion of an interval in a partial monounary algebra is introduced and pairs ( A , f ) , ( A , g ) of partial monounary algebras are investigated such that each interval in ( A , f ) is also an interval in ( A , g ) , and conversely.

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