Demi-pseudocomplemented lattices: Principal congruences and subdirect irreducibility
type: Item
instance of: scholarly article
title: Demi-pseudocomplemented lattices: Principal congruences and subdirect irreducibility
zbMATH Open document ID: 0701.06009
DOI: 10.1007/BF01182452
author: Hanamantagouda P. Sankappanavar
published in: Algebra Universalis
publication date: 1990-01-01T00:00:00Z
review text: In this (essentially self-contained) paper the author continues his earlier investigations on demi-p-lattices [J. Symb. Logic 52, 712-724 (1987; Zbl 0628.06011)]. In Section 2, definitions and some new characterizations of demi-p-lattices, almost p-lattices and p-lattices are presented. Main results of this paper are to characterize the principal congruences on demi-p-lattices, which extends the corresponding characterization for p-lattices [\textit{H. Lakser}, Proc. Am. Math. Soc. 37, 32-36 (1973; Zbl 0269.06005)]. As an application of this characterization it is shown that the variety of demi-p-lattices has equationally definable principal congruences - a result which strengthens an earlier result that this variety has the congruence extension property. Section 4 describes a construction of a class of subdirectly irreducible demi-p-lattices and Section 5 uses this construction and the characterization of principal congruences (obtained in Section 3) to characterize the subdirectly irreducible demi-p-lattices, thus giving a partial solution to one of the problems raised in the author's earlier paper [loc. cit.]. This characterization extends the corresponding result of Lakser [loc. cit.] which was proved for p-lattices.
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 4148160
zbMATH Keywords: subdirect irreducibility
zbMATH Keywords: demi-p-lattices
zbMATH Keywords: almost p-lattices
zbMATH Keywords: principal congruences
reviewed by: Richard A. Aló
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4148160