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Displaying 21 – 40 of 74

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

Enriched MV-algebras.

Ulrich Höhle (1995)

Mathware and Soft Computing

This paper introduces the structure of enriched MV-algebras and studies on this basis various relations between sigma-complete MV-algebras and T-tribes.

Fan-Gottesman type compactification of frames

Dharmanand Baboolal (1990)

Commentationes Mathematicae Universitatis Carolinae

Free almost-p-lattices

Hernando Gaitan (1996)

Czechoslovak Mathematical Journal

Free $Q$ -distributive lattice over an $n$ -element chain.

Monteiro, Luiz, Abad, Manuel, Zander, Marta (2004)

Portugaliae Mathematica. Nova Série

Functional completeness in pseudocomplemented de Morgan algebras

Klaus Denecke (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

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,...

Generalizations of Boolean algebras. An attribute exploration

Léonard Kwuida, Christian Pech, Heiko Reppe (2006)

Mathematica Slovaca

Maximal and essential ideals of MV-álgebras.

Cheong Seng Hoo (1995)

Mathware and Soft Computing

Maximal MV-algebras.

Alexandru Filipoiu, George Georgescu, Ada Lettieri (1997)

Mathware and Soft Computing

In this paper we define maximal MV-algebras, a concept similar to the maximal rings and maximal distributive lattices. We prove that any maximal MV-algebra is semilocal, then we characterize a maximal MV-algebra as finite direct product of local maximal MV-algebras.

Modal extensions of Heyting algebras

R. Beazer, D. S. Macnab (1979)

Colloquium Mathematicae

Modal operators on symmetrical Heyting algebras

Luisa Iturrioz (1982)

Banach Center Publications

Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo, Nora Oliva, Alicia Ziliani (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Modal pseudocomplemented De Morgan algebras (or $m p M$ -algebras for short) are investigated in this paper. This new equational class of algebras was introduced by A. V. Figallo and P. Landini ([Figallo, A. V., Landini, P.: Notes on $4$ -valued modal algebras Preprints del Instituto de Ciencias Básicas, Univ. Nac. de San Juan 1 (1990), 28–37.]) and they constitute a proper subvariety of the variety of all pseudocomplemented De Morgan algebras satisfying $x \land {(\sim x)}^{*} = {(\sim (x \land {(\sim x)}^{*}))}^{*}$ . Firstly, a topological duality for these algebras...

Molecules and linerly ordered ideals of MV-algebras.

C. S. Hoo (1997)

Publicacions Matemàtiques

We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime.

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...

Negation operations definable on finite distributive lattices

Priestley, H.A., Bordalo, G. (1992)

Portugaliae 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 certain construction of MS-algebras.

Haviar, Miroslav (1994)

Portugaliae Mathematica

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

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