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A Cantor-Bernstein theorem for $σ$ -complete MV-algebras

Anna de Simone, Daniele Mundici, Mirko Navara (2003)

Czechoslovak Mathematical Journal

The Cantor-Bernstein theorem was extended to $σ$ -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to $σ$ -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.

A certain Galois connection and weak automorphisms

Kazimierz Głazek (1997)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A glimpse of deductive systems in algebra

Dumitru Buşneag, Sergiu Rudeanu (2010)

Open Mathematics

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras...

Associative $n$ -dimensional copulas

Andrea Stupňanová, Anna Kolesárová (2011)

Kybernetika

The associativity of $n$ -dimensional copulas in the sense of Post is studied. These copulas are shown to be just $n$ -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.

Closure Łukasiewicz algebras

Abad Manuel, Cimadamore Cecilia, Díaz Varela José, Rueda Laura, Suardíaz Ana (2005)

Open Mathematics

In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.

Complete generators and maximal completions of $M V$ -algebras

Ján Jakubík (1998)

Czechoslovak Mathematical Journal

Connections between ideals of non-commutative generalizations of $M V$ -algebras and ideals of their underlying lattices

Jiří Rachůnek (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

DMF-algebras: representation and topological characterization

Maurizio Negri (1998)

Bollettino dell'Unione Matematica Italiana

Gli insiemi parziali sono coppie $(A, B)$ di sottoinsiemi di $X$ , dove $A \cap B \neq 0$ . Gli insiemi parziali su $X$ costituiscono una DMF-algebra, ossia un'algebra di De Morgan in cui la negazione ha un solo punto fisso. Dimostriamo che ogni DMF-algebra è isomorfa a un campo di insiemi parziali. Utilizzando gli insiemi parziali su $X$ come aperti, introduciamo il concetto di spazio topologico parziale su $X$ . Infine associamo ad ogni DMF-algebra $A$ uno spazio topologico parziale i cui clopen compatti costituiscono un campo d'insiemi...

DRl-semigroups and $M V$ -algebras

Jiří Rachůnek (1998)

Czechoslovak Mathematical Journal

Functional monadic $n$ -valued Łukasiewicz algebras

A. V. Figallo, Claudia A. Sanza, Alicia Ziliani (2005)

Mathematica Bohemica

Some functional representation theorems for monadic $n$ -valued Łukasiewicz algebras (qLk $_{n}$ -algebras, for short) are given. Bearing in mind some of the results established by G. Georgescu and C. Vraciu (Algebre Boole monadice si algebre Łukasiewicz monadice, Studii Cercet. Mat. 23 (1971), 1027–1048) and P. Halmos (Algebraic Logic, Chelsea, New York, 1962), two functional representation theorems for qLk $_{n}$ -algebras are obtained. Besides, rich qLk $_{n}$ -algebras are introduced and characterized. In addition,...

Homomorphism kernels of a tetravalent modal algebra

Loureiro, Isabel (1980)

Portugaliae mathematica

Hoops and their implicational reducts (abstract)

W. Bloki, I. Ferreirim (1993)

Banach Center Publications

Logique trivalente de Lukasiewicz

Denise Becchio (1978)

Annales scientifiques de l'Université de Clermont. Mathématiques

Modal operators on symmetrical Heyting algebras

Luisa Iturrioz (1982)

Banach Center Publications

Monadic $n \times m$ -valued Łukasiewicz-Moisil algebras

A. V. Figallo, Claudia A. Sanza (2012)

Mathematica Bohemica

Here we initiate an investigation into the class $m L M_{n \times m}$ of monadic $n \times m$ -valued Łukasiewicz-Moisil algebras (or $m L M_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$ -valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $m L M_{n \times m}$ is a discriminator variety and as a consequence, the...

MV-algebras with additive closure operators

Jiří Rachůnek, Filip Švrček (2000)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Notes on monadic $n$ -valued Łukasiewicz algebras

A. V. Figallo, Inés Pascual, Alicia Ziliani (2004)

Mathematica Bohemica

A topological duality for monadic $n$ -valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz $n$ -valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of $Q$ -distributive lattices and $Q$ -homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets...

On a representation theorem of De Morgan algebras by fuzzy sets.

Francesc Esteva (1981)

Stochastica

Once the concept of De Morgan algebra of fuzzy sets on a universe X can be defined, we give a necessary and sufficient condition for a De Morgan algebra to be isomorphic to (represented by) a De Morgan algebra of fuzzy sets.

On archimedean $M V$ -algebras

Ján Jakubík (1998)

Czechoslovak Mathematical Journal

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