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Bounded lattices with antitone involutions and properties of MV-algebras

100%

Chajda I. , Emanovský P.

Discussiones Mathematicae - General Algebra and Applications

2004

tom 24

nr 1

31-42

We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.

Commutative directoids with sectionally antitone bijections

100%

Chajda I. , Kolařík M. , Radeleczki S.

Discussiones Mathematicae - General Algebra and Applications

2008

tom 28

nr 1

77-89

We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.

Endomorphisms and subalgebras of Tarski algebras

100%

Gaitán H.

Reports on Mathematical Logic

2015

tom Vol. 50

31--39

In this note we prove that a Tarski algebra is determined by the monoid of its endomorphisms as well as by the lattice of its subalgebras.

Endomorphisms of implication algebras

88%

Gaitán H.

Demonstratio Mathematica

2014

tom Vol. 47, nr 2

284--288

In this note we prove that if two implication algebras have isomorphic monoids of endomorphisms then they are isomorphic.

Implication algebras

88%

Chajda I.

Discussiones Mathematicae - General Algebra and Applications

2006

tom 26

nr 2

141-153

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.