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Weak-quasi-Stone algebras

✍ Scribed by Sergio A. Celani; Leonardo M. Cabrer

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 125 KB
Volume: 55
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710092

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✦ Synopsis

Abstract

In this paper we shall introduce the variety WQS of weak‐quasi‐Stone algebras as a generalization of the variety QS of quasi‐Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬‐lattices to give a duality for WQS. We prove that a weak‐quasi‐Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and subdirectly irreducible algebras (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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