A note on the weak subalgebra lattice of a unary algebra with constants
type: Item
instance of: scholarly article
zbMATH Open document ID: 0999.08003
author: Konrad Pióro
publication date: 2001-11-05T00:00:00Z
Mathematics Subject Classification ID: 08A60
Mathematics Subject Classification ID: 08A55
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 1668780
zbMATH Keywords: digraph
zbMATH Keywords: strong and weak subalgebras
zbMATH Keywords: subalgebra lattices
zbMATH Keywords: unary algebra
zbMATH Keywords: partial algebra
MaRDI profile type: Publication
title: A note on the weak subalgebra lattice of a unary algebra with constants
published in: Publicationes Mathematicae Debrecen
review text: Investigations of relationships between (total) algebras or varieties of algebras and their subalgebra lattices are one of the most interesting parts of universal algebra. NEWLINENEWLINENEWLINEA description of algebras or varieties of algebras, classical algebras -- Boolean algebras, groups and modules which have special subalgebra lattices (i.e. modular, distributive, etc.) -- was given by \textit{P. P. Palfy} [Algebra Univers. 27, 220-229 (1990; Zbl 0708.08002)] and \textit{E. Lukács} and \textit{P. P. Palfy} [Arch. Math. 46, 18-19 (1986; Zbl 0998.20500)]. NEWLINENEWLINENEWLINEIn the present paper the author proves the following results: Let \(A\) be a total and locally finite algebra having finitely many constants and only unary operations. Then for every partial algebra \(B\) of the same type, if the weak subalgebra lattices of \(A\) and \(B\) are isomorphic, then their strong subalgebra lattices are also isomorphic, and \(B\) is also total and locally finite.
description: scientific article; zbMATH DE number 1668780