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Some problems for measures on non-standard algebraic structures

Maria Gabriella Graziano (2000)

Bollettino dell'Unione Matematica Italiana

Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...

Some properties of congurence relations on orthomodular lattices

Gerhard Dorfer (2001)

Discussiones Mathematicae - General Algebra and Applications

In this paper congruences on orthomodular lattices are studied with particular regard to analogies in Boolean algebras. For this reason the lattice of p-ideals (corresponding to the congruence lattice) and the interplay between congruence classes is investigated. From the results adduced there, congruence regularity, uniformity and permutability for orthomodular lattices can be derived easily.

Some properties of Eulerian lattices

R. Subbarayan, A. Vethamanickam (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.

Some properties of Lorenzen ideal systems

Aleka Kalapodi, Angeliki Kontolatou, Jiří Močkoř (2000)

Archivum Mathematicum

Let G be a partially ordered abelian group ( p o -group). The construction of the Lorenzen ideal r a -system in G is investigated and the functorial properties of this construction with respect to the semigroup ( R ( G ) , ⊕ , ≤ ) of all r -ideal systems defined on G are derived, where for r , s ∈ R ( G ) and a lower bounded subset X ⊆ G , X r ⊕ s = X r ∩ X s . It is proved that Lorenzen construction is the natural transformation between two functors from the category of p o -groups with special morphisms into the category of abelian ordered semigroups.

Some properties of residuated lattices

Radim Bělohlávek (2003)

Czechoslovak Mathematical Journal

We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.

Some properties of the weak subalgebra lattice of a partial algebra of a fixed type

Konrad Pióro (2002)

Archivum Mathematicum

We investigate, using results from [[p3]], when a given lattice is isomorphic to the weak subalgebra lattice of a partial algebra of a fixed type. First, we reduce this problem to the question when hyperedges of a hypergraph can be directed to a form of directed hypergraph of a fixed type. Secondly, we show that it is enough to consider some special hypergraphs. Finally, translating these results onto the lattice language, we obtain necessary conditions for our algebraic problem, and also, we completely...

Some remarks on distributive semilattices

Sergio A. Celani, Ismael Calomino (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....

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