Efficient generation of the ring of invariants
type: Item
instance of: scholarly article
title: Efficient generation of the ring of invariants
zbMATH Open document ID: 0846.15014
author: Shou-Jen Hu
author: Ming-Chang Kang
published in: Journal of Algebra
publication date: 1996-09-23T00:00:00Z
review text: By using the Binet-Minc formula in the theory of permanents, the author proves David Richman's theorem: Let \(G\) be a finite group on \(A:= R(a_1, \dots, a_r)\), where \(R\) is any commutative ring with \(1/|G|!\in R\) (\(|G|\) denotes the order of \(G\)). Then the ring of invariants \(A^G\) is generated over \(R\) by \(\sum_{\sigma\in G} \sigma (a_1^{\alpha_1} a_2^{\alpha_2} \dots a_r^{\alpha_r})\), where \(\alpha_1+ \dots +\alpha_r\leq |G|\). In the course of discussion, applications of permanents to other problems related to invariants, e.g., the properties of symmetric polynomials, are also given.
reviewed by: Yang Yingchen
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 869782
zbMATH Keywords: commutative ring
zbMATH Keywords: polynomial ring
zbMATH Keywords: Binet-Minc formula
zbMATH Keywords: permanents
zbMATH Keywords: ring of invariants
MaRDI profile type: Publication
full work available at URL: jabr.1996.0071
OpenAlex ID: W1971181578
DOI: 10.1006/JABR.1996.0071
description: scientific article; zbMATH DE number 869782