Waring's problem for algebras over fields
type: Item
instance of: scholarly article
title: Waring's problem for algebras over fields
zbMATH Open document ID: 0624.10049
DOI: 10.1016/0022-314X(87)90085-0
published in: Journal of Number Theory
publication date: 1987-01-01T00:00:00Z
review text: For a ring A let \(w_ k(A)\) denote the smallest s such that every sum of kth powers in A is a sum of s kth powers; let \(v_ k(A)\) denote the corresponding infimum for the sum-or-difference of kth powers. This paper gives a detailed study of \(v_ k(A)\) and \(w_ k(A)\) when A is an algebra over a field F. The main result can be stated as follows: \(v_ k(A)\leq k^ 3\) when A is commutative and either F is infinite or A has transcendence degree 1 over F. This statement swallows up several more precise results, which give sharper upper bounds in many situations of interest.
Mathematics Subject Classification ID: 11C99
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 4012751
zbMATH Keywords: Waring's problem for rings
author: L. N. Vaserstein
reviewed by: Charles Small
MaRDI profile type: Publication
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full work available at URL: 0022-314x(87)90085-0
OpenAlex ID: W2075119953
description: scientific article; zbMATH DE number 4012751