scholarly journals Orthomodular lattices can be converted into left residuated l-groupoids

2017 ◽  
Vol 18 (2) ◽  
pp. 685 ◽  
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Orthomodular Lattices

Roughness in Orthomodular Lattices

2012 ◽  
Vol 2 (1) ◽  
pp. 9
Author(s):  
E. K. R Nagarajan ◽  
D. Umadevi
Keyword(s):  
Orthomodular Lattices

scholarly journals Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

scholarly journals Rough Approximation Operators on a Complete Orthomodular Lattice

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 164
Author(s):  
Songsong Dai
Keyword(s):  
Boolean Algebra ◽  
Orthomodular Lattice ◽  
Orthomodular Lattices ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Distributive Law ◽  
Complete Orthomodular Lattice ◽  
The Relationship

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

Semigroups Co-Ordinatizing Orthomodular Geometries

1965 ◽  
Vol 17 ◽  
pp. 40-51 ◽  
Author(s):  
D. J. Foulis
Keyword(s):  
Orthomodular Lattice ◽  
Orthomodular Lattices

In (2, 3, 4, and 5), the author has established a connection between orthomodular lattices and Baer *-semigroups. In brief, the connection is as follows. The lattice of closed projections of any Baer *-semigroup forms an orthomodular lattice. Conversely, if L is any orthomodular lattice, there exists a Baer *-semigroup S which co-ordinatizes L in the sense that L is isomorphic to the lattice of closed projections in S. In this note we shall assume that the reader is familiar with the results and the notation of the quoted papers.

Central and Exchange Properties of Orthomodular Lattices

1980 ◽  
Vol 97 (1) ◽  
pp. 247-251 ◽  
Author(s):  
Ladislav Beran
Keyword(s):  
Orthomodular Lattices ◽  
Exchange Properties

L-algebras and topology

2021 ◽  
Author(s):  
Wolfgang Rump
Keyword(s):  
Mapping Class Groups ◽  
Unitary Groups ◽  
Mapping Class ◽  
Heyting Algebras ◽  
Baxter Equation ◽  
Prime Spectrum ◽  
Class Groups ◽  
Orthomodular Lattices ◽  
And Topology ◽  
Torsion Free

[Formula: see text]-algebras are based on an equation which is fundamental in the construction of various torsion-free groups, including spherical Artin groups, Riesz groups, certain mapping class groups, para-unitary groups, and structure groups of set-theoretic solutions to the Yang–Baxter equation. A topological study of [Formula: see text]-algebras is initiated. A prime spectrum is associated to certain (possibly all) [Formula: see text]-algebras, including three classes of [Formula: see text]-algebras where the ideals are determined in a more explicite fashion. Known results on orthomodular lattices, Heyting algebras, or quantales are extended and revisited from an [Formula: see text]-algebraic perspective.

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