scholarly journals On the dualization in distributive lattices and related problems

2021 ◽  
Vol 300 ◽  
pp. 85-96
Author(s):  
Oscar Defrain ◽  
Lhouari Nourine ◽  
Takeaki Uno
Keyword(s):  
Distributive Lattices

L-Fuzzy Filters of Almost Distributive Lattices

2018 ◽  
Vol 8 (1) ◽  
pp. 35
Author(s):  
U. M. Swamy ◽  
Ch. Santhi Sundar Raj ◽  
A. Natnael Teshale
Keyword(s):  
Distributive Lattices ◽  
Fuzzy Filters

scholarly journals Priestley duality for MV-algebras and beyond

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wesley Fussner ◽  
Mai Gehrke ◽  
Samuel J. van Gool ◽  
Vincenzo Marra
Keyword(s):  
Large Class ◽  
Order Conditions ◽  
Enriched Environment ◽  
Priestley Duality ◽  
Distributive Lattices ◽  
First Order ◽  
Dual Spaces ◽  
Binary Operations ◽  
New Perspective ◽  
Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

scholarly journals The Central Decomposition of FD01(n)

Order ◽  
2021 ◽  
Author(s):  
Peter Köhler
Keyword(s):  
Distributive Lattices ◽  
Finitely Generated ◽  
Finite Distributive Lattices

AbstractThe paper presents a method of composing finite distributive lattices from smaller pieces and applies this to construct the finitely generated free distributive lattices from appropriate Boolean parts.

Congruence relations on almost distributive lattices-II

2019 ◽  
pp. 2150005
Author(s):  
Gezahagne Mulat Addis
Keyword(s):  
Distributive Lattice ◽  
Congruence Relation ◽  
Congruence Class ◽  
Distributive Lattices ◽  
Ideal Formula ◽  
Congruence Relations

For a given ideal [Formula: see text] of an almost distributive lattice [Formula: see text], we study the smallest and the largest congruence relation on [Formula: see text] having [Formula: see text] as a congruence class.

scholarly journals Stone algebras form an equational class: (Remarks on Lattice Theory III)

1969 ◽  
Vol 9 (3-4) ◽  
pp. 308-309 ◽  
Author(s):  
G. Grätzer
Keyword(s):  
Lattice Theory ◽  
Equational Class ◽  
Distributive Lattices ◽  
Image Position

To prove the statement given in the title take a set Σ1 of identities characterizing distributive lattices 〈L; ∨, ∧, 0, 1〉 with 0 and 1, and let Then is Σ redundant set of identities characterizing Stone algebras = 〈L; ∨, ∧, *, 0, 1〉. To show that we only have to verify that for a ∈ L, a* is the pseudo-complement of a. Indeed, a ∧ a* 0; now, if a ∧ x = 0, then a* ∨ x* 0* = 1, and a** ∧ = 1* = 0; since a** is the complement of a*, the last identity implies x** ≦ a*, thus x ≦ x** ≦ a*, which was to be proved.

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