Some applications of higher commutators in Mal'cev algebras
type: Item
instance of: scholarly article
title: Some applications of higher commutators in Mal'cev algebras
zbMATH Open document ID: 1206.08003
author: Erhard Aichinger
author: Nebojša Mudrinski
published in: Algebra Universalis
publication date: 2010-11-22T00:00:00Z
review text: Many properties of higher commutators in congruence-permutable varieties are derived. Let \(A\) be a finite nilpotent algebra of finite type that is a product of algebras of prime power order and generates a congruence-modular variety. Using higher commutators, the following results are proved: There is an algorithm that decides whether every congruence-preserving function on \(A\) is a polynomial function on \(A\) or not. The problem of deciding if two given polynomial terms of \(A\) induce the same function has polynomial time complexity in the length of the input terms.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 5818038
zbMATH Keywords: higher commutator
zbMATH Keywords: congruence-permutable variety
zbMATH Keywords: congruence-modular variety
zbMATH Keywords: congruence-preserving function
zbMATH Keywords: polynomial function
zbMATH Keywords: polynomial term
zbMATH Keywords: Mal'tsev algebras
zbMATH Keywords: nilpotent algebra
MaRDI profile type: Publication
full work available at URL: s00012-010-0084-1
OpenAlex ID: W1971935730
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DOI: 10.1007/S00012-010-0084-1
description: scientific article; zbMATH DE number 5818038