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Characterizations of 0-distributive posets

Vinayak V. Joshi, B. N. Waphare (2005)

Mathematica Bohemica

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

Classes of filters in generalizations of commutative fuzzy structures

Jiří Rachůnek, Dana Šalounová (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Bounded commutative residuated lattice ordered monoids ( R -monoids) are a common generalization of 𝐵𝐿 -algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative R -monoids.

Classes of fuzzy filters of residuated lattice ordered monoids

Jiří Rachůnek, Dana Šalounová (2010)

Mathematica Bohemica

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of BL -algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding...

Classification of the regular De Morgan algebras of fuzzy sets.

Francesc Esteva, Núria Piera (1984)

Stochastica

A characterization of regular lattices of fuzzy sets and their isomorphisms is given in Part I. A characterization of involutions on regular lattices of fuzzy sets and the isomorphisms of De Morgan algebras of fuzzy sets is given in Part II. Finally all classes of De Morgan algebras of fuzzy sets with respect to isomorphisms are completely described.

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.

Coaxial filters of distributive lattices

M. Sambasiva Rao (2023)

Archivum Mathematicum

Coaxial filters and strongly coaxial filters are introduced in distributive lattices and some characterization theorems of p m -lattices are given in terms of co-annihilators. Some properties of coaxial filters of distributive lattices are studied. The concept of normal prime filters is introduced and certain properties of coaxial filters are investigated. Some equivalent conditions are derived for the class of all strongly coaxial filters to become a sublattice of the filter lattice.

Cocycle condition for multi-pullbacks of algebras

Piotr M. Hajac, Bartosz Zieliński (2012)

Banach Center Publications

Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorphism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks...

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