Displaying similar documents to “Some properties of residuated lattices”

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

Leonardo Cabrer, Sergio Celani (2006)

Open Mathematics

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In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space. ...

Monadic basic algebras

Ivan Chajda, Miroslav Kolařík (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The concept of monadic MV-algebra was recently introduced by A. Di Nola and R. Grigolia as an algebraic formalization of the many-valued predicate calculus described formerly by J. D. Rutledge [9]. This was also genaralized by J. Rachůnek and F. Švrček for commutative residuated ℓ -monoids since MV-algebras form a particular case of this structure. Basic algebras serve as a tool for the investigations of much more wide class of non-classical logics (including MV-algebras, orthomodular...

Interior and Closure Operators on Commutative Bounded Residuated Lattices

Jiří Rachůnek, Zdeněk Svoboda (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.

Interior and closure operators on bounded residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2014)

Open Mathematics

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Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and...

An algebraic version of the Cantor-Bernstein-Schröder theorem

Hector Freytes (2004)

Czechoslovak Mathematical Journal

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The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to σ -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder...

Monotone modal operators on bounded integral residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2012)

Mathematica Bohemica

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Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.