Valuations and hypersubstitutions
type: Item
instance of: scholarly article
title: Valuations and hypersubstitutions
zbMATH Open document ID: 1051.08004
published in: Southeast Asian Bulletin of Mathematics
publication date: 2004-05-27T00:00:00Z
review text: A valuation of a term \(t\) is a non-negative integer which expresses in a certain sense the complexity of \(t\) (it can be the number of operations occurring in \(t\), the number of variables, etc). A hypersubstitution \(\sigma\) is called increasing with respect to a valuation \(v\) if \(v(t)\leq v(\overline\sigma(t))\). This determines a Galois connection between the set of all hypersubstitutions of type \(\mathcal T\) and the set \(\text{Val}({\mathcal T})\) of all valuations of type \(\mathcal T\). The result is applied to produce a monoid \(N\) for which the \(k\)-normalized variety of an \(M\)-solid variety \(\mathcal V\) with respect to a given valuation is \(N\)-solid.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08A70
zbMATH DE Number: 2067233
zbMATH Keywords: terms
zbMATH Keywords: valuations
zbMATH Keywords: hypersubstitution
zbMATH Keywords: \(k\)-normalization
zbMATH Keywords: \(M\)-solid varieties
zbMATH Keywords: Galois connection
author: Klaus Denecke
author: Shelly L. Wismath
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2067233