scholarly journals N-prime spectrum of stone Almost Distributive Lattices

2021 ◽  
Vol 41 (2) ◽  
pp. 299
Author(s):  
Ravi Kumar Bandaru ◽  
N. Rafi ◽  
M. Srujana
Keyword(s):  
Distributive Lattices ◽  
Prime Spectrum

The Duality of Distributive Continuous Lattices

1980 ◽  
Vol 32 (2) ◽  
pp. 385-394 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Dual Space ◽  
Boolean Algebras ◽  
Distributive Lattices ◽  
Continuous Lattice ◽  
Prime Spectrum ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Continuous Lattices ◽  
Prime Elements

Various aspects of the prime spectrum of a distributive continuous lattice have been discussed extensively in Hofmann-Lawson [7]. This note presents a perhaps optimally direct and self-contained proof of one of the central results in [7] (Theorem 9.6), the duality between distributive continuous lattices and locally compact sober spaces, and then shows how the familiar dualities of complete atomic Boolean algebras and bounded distributive lattices derive from it, as well as a new duality for all continuous lattices. As a biproduct, we also obtain a characterization of the topologies of compact Hausdorff spaces.Our approach, somewhat differently from [7], takes the open prime filters rather than the prime elements as the points of the dual space. This appears to have conceptual advantages since filters enter the discussion naturally, besides being a well-established tool in many similar situations.

scholarly journals β-prime spectrum of stone Almost Distributive Lattices

2020 ◽  
Vol 40 (2) ◽  
pp. 311
Author(s):  
Ravi Kumar Bandaru ◽  
N. Rafi
Keyword(s):  
Distributive Lattices ◽  
Prime Spectrum

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

Prime O-Ideals of Distributive Lattices

2012 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Mukkamala Sambasiva Rao
Keyword(s):  
Distributive Lattices

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.

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