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Distributive Lattices with a Negation Operator

✍ Scribed by Sergio Arturo Celani

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 736 KB
Volume: 45
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19990450206

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✦ Synopsis

In this note we introduce and study algebras ( L , V, A, 1, 0,l) of type (2,2,1,1,1) such that ( L , V, A , 0 , l ) is a bounded distributive lattice and -,is an operator that satisfies the conditions -,(a V b ) = -,a A -,b and -0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.

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