Bounded and well-placed theories in the lattice of equational theories
type: Item
instance of: scholarly article
title: Bounded and well-placed theories in the lattice of equational theories
zbMATH Open document ID: 0696.08003
DOI: 10.1007/BF01211838
published in: Algebra Universalis
publication date: 1989-01-01T00:00:00Z
review text: Let T be a fully invariant congruence relation on a term algebra \({\mathfrak A}\) of similarity type \(\rho\), i.e. an equational theory of type \(\rho\). The theory T is said to be bounded iff the number of orbits of \({\mathfrak A}/T\) under the (induced) action of Aut(\({\mathfrak A})\) is finite. The class of bounded theories and some of its subclasses, called well-placed, are studied. In particular, it turned out that in the case of a type with only one operation symbol and without constant symbol, the theory T is bounded iff it is an extension of a well-placed theory. Another result of the paper says that if \(\rho\) is the same as above, then, under the additional assumption that T is absorptive, i.e. (x,t)\(\in T\) for some term t which is not a variable, the theory T is bounded iff it is well- placed.
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08B20
zbMATH DE Number: 4139824
zbMATH Keywords: bounded variety
zbMATH Keywords: absorptive variety
zbMATH Keywords: single algebra
zbMATH Keywords: term algebra
zbMATH Keywords: equational theory
zbMATH Keywords: bounded theories
zbMATH Keywords: well-placed theory
author: Jaroslav Ježek
author: George F. McNulty
reviewed by: Ernest Płonka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01211838
OpenAlex ID: W2070357850
description: scientific article; zbMATH DE number 4139824