The number of homomorphic images of certain Golod groups and algebras
type: Item
instance of: scholarly article
title: The number of homomorphic images of certain Golod groups and algebras
zbMATH Open document ID: 0862.16017
DOI: 10.1007/BF03322220
author: Lakhdar Hammoudi
published in: Results in Mathematics
publication date: 1996-10-30T00:00:00Z
review text: An algebra \(A\) is called a Golod \(d\)-algebra (\(d>1\)), if it is \(d\)-generated and nonnilpotent, but any \((d-1)\)-generated subalgebra of \(A\) is nilpotent. Let \(F\) be a free algebra over a field \(k\), \(I\) be an ideal, generated by a sequence of polynomials \(f_1,f_2,\dots\), Golod proved that under the well known Golod condition the algebra \(A/I\) is infinite dimensional. Theorem 1. For any finite set \(M\) of integers greater or equal to \(d\), there exists a Golod \(d\)-algebra such that for any \(d'\) from \(M\), \(A\) contains a Golod \(d'\)-algebra (ideal) \(B\), with the Golod condition for \(A/B\). Theorem 2. For any \(d>1\) and any field there exists a Golod \(d\)-algebra having a continuum of residually finite pairwise nonisomorphic homomorphic images.
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E26
zbMATH DE Number: 920807
zbMATH Keywords: Golod \(d\)-algebras
zbMATH Keywords: residually finite homomorphic images
zbMATH Keywords: free algebras
zbMATH Keywords: Golod condition
reviewed by: Leonid A. Bokut'
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 920807