Natural continuity space structures on dual Heyting algebras
Natural dualities for varieties of distributive lattices with a quantifier
N-compact frames
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
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.
Negation operations definable on finite distributive lattices
Noetherian and Artinian pseudo MV-algebras
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.
Nonstandard implication algebras
Normal skew lattices.
Normalization of basic algebras
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
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
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 Modular and Distributive Equalities in Lattices
Note on -filters in distributive nearlattices
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 characterization of paracompact frames
Notes on Kuratowski-Mrówka theorems in point-free context
Notes on lattices of frame tolerances
Notes on monadic -valued Łukasiewicz algebras
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...