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N-compact frames

Greg M. Schlitt (1991)

Commentationes Mathematicae Universitatis Carolinae

We investigate notions of -compactness for frames. We find that the analogues of equivalent conditions defining -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘-cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial -compactness form a much larger class, and better embody what ‘-compact frames’ should be. This latter property is expressible without reference...

Negation in bounded commutative -monoids

Jiří Rachůnek, Vladimír Slezák (2006)

Czechoslovak Mathematical Journal

The class of commutative dually residuated lattice ordered monoids (-monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded -monoids is introduced, its properties are studied and the sets of regular and dense elements of -monoids are described.

Noetherian and Artinian pseudo MV-algebras

Grzegorz Dymek (2008)

Discussiones Mathematicae - General Algebra and Applications

The notions of Noetherian pseudo MV-algebras and Artinian pseudo MV-algebras are introduced and their characterizations are established. Characterizations of them via fuzzy ideals are also given.

Normalization of basic algebras

Miroslav Kolařík (2008)

Discussiones Mathematicae - General Algebra and Applications

We consider algebras determined by all normal identities of basic algebras. For such algebras, we present a representation based on a q-lattice, i.e., the normalization of a lattice.

Normalization of -algebras

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

Mathematica Bohemica

We consider algebras determined by all normal identities of -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 -lattice, and another one based on a normalization of a lattice-ordered group.

Note on dense covers in the category of locales

Jan Paseka (1994)

Commentationes Mathematicae Universitatis Carolinae

In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.

Note on -filters in distributive nearlattices

Ismael Calomino (2019)

Mathematica Bohemica

In this short paper we introduce the notion of -filter in the class of distributive nearlattices and we prove that the -filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators.

Notes on monadic -valued Łukasiewicz algebras

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

Mathematica Bohemica

A topological duality for monadic -valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz -valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of -distributive lattices and -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...

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