Ockham algebras with double pseudocomplementation
type: Item
instance of: scholarly article
title: Ockham algebras with double pseudocomplementation
zbMATH Open document ID: 1134.06009
author: N. E. Zubov
published in: Algebra Universalis
publication date: 2007-01-29T00:00:00Z
review text: A (universal) algebra \((L; \vee, \wedge, f, ^*, ^+, 0, 1)\) is called a double pseudocomplemented Ockham algebra (shortly, \textbf{dpO}), if \(L=(L; \vee, \wedge, 0, 1)\) is a bounded distributive lattice together with three unary operations, \(f\), \(^*\) and \(^+\), such that (i) \((L; f)\) is an Ockham algebra, (ii) \(^*\) is the operation of pseudocomplementation, (iii) \(^+\) is the operation of dual pseudocomplementation, (iv) \(f\) and \(^*\) commute and (v) \(f\) and \(^+\) commute. The author describes (i) the principal congruence relations in \textbf{dpO} and (ii) characterizes the subdirectly irreducible algebras that belong to the subvariety of \textbf{dpO} defined by the identity \(f=f^3.\)
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 06D15
zbMATH DE Number: 5119637
zbMATH Keywords: Ockham algebras
zbMATH Keywords: double p-algebras
zbMATH Keywords: subdirectly irreducible
reviewed by: Tibor Katriňák
MaRDI profile type: Publication
full work available at URL: s00012-006-1968-y
OpenAlex ID: W1971227397
DOI: 10.1007/S00012-006-1968-Y
description: scientific article; zbMATH DE number 5119637