Displaying similar documents to “Higher degrees of distributivity in M V -algebras”

On intervals and isometries of M V -algebras

Ján Jakubík (2002)

Czechoslovak Mathematical Journal

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Let Int 𝒜 be the lattice of all intervals of an M V -algebra 𝒜 . In the present paper we investigate the relations between direct product decompositions of 𝒜 and (i) the lattice Int 𝒜 , or (ii) 2-periodic isometries on 𝒜 , respectively.

Distributivity of bounded lattices with sectionally antitone involutions

Ivan Chajda (2005)

Discussiones Mathematicae - General Algebra and Applications

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We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.

Bounded lattices with antitone involutions and properties of MV-algebras

Ivan Chajda, Peter Emanovský (2004)

Discussiones Mathematicae - General Algebra and Applications

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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...