Displaying similar documents to “The Role of Halaš Identity in Orthomodular Lattices”

Coaxial filters of distributive lattices

M. Sambasiva Rao (2023)

Archivum Mathematicum

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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. ...

On systems of congruences on principal filters of orthomodular implication algebras

Radomír Halaš, Luboš Plojhar (2007)

Mathematica Bohemica

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Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.