Displaying similar documents to “Distributivity of bounded lattices with sectionally antitone involutions”

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...

Unicidad de implicación de álgebra-MV y negación de De Morgan.

Néstor G. Martínez, Hilary A. Priestley (1995)

Mathware and Soft Computing

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It is shown that the implication of an MV-algebra is determined by de Morgan negation operations on a family of quotients of the given algebra; these quotients may be taken to be totally ordered. Certain existing results on the uniqueness of an MV-algebra implication are thereby elucidated and new criteria for uniqueness derived. These rely on a characterisation of chains on which a de Morgan negation is necessarily unique.

Higher degrees of distributivity in M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

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In this paper we deal with the of an M V -algebra 𝒜 , where α and β are nonzero cardinals. It is proved that if 𝒜 is singular and ( α , 2 ) -distributive, then it is . We show that if 𝒜 is complete then it can be represented as a direct product of M V -algebras which are homogeneous with respect to higher degrees of distributivity.

A characterization of commutative basic algebras

Ivan Chajda (2009)

Mathematica Bohemica

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A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.

Normalization of M V -algebras

Ivan Chajda, Radomír Halaš, Jan Kühr, Alena Vanžurová (2005)

Mathematica Bohemica

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We consider algebras determined by all normal identities of M V -algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a q -lattice, and another one based on a normalization of a lattice-ordered group.