The trace as an algebra homomorphism
type: Item
instance of: scholarly article
title: The trace as an algebra homomorphism
zbMATH Open document ID: 0605.16018
author: Howard Osborn
published in: L'Enseignement Mathématique. 2e Série
publication date: 1985-01-01T00:00:00Z
review text: Let V be an (appropriately restricted) module over a commutative ring R with unit. Then, denoting by \(\Lambda^ pV\) the p-th exterior power of V and considering the direct sum \(\coprod_ pEnd \Lambda^ pV\), a product on this space is defined, such that with a suitable definition of the operator trace: \(\coprod_ pEnd \Lambda^ pV\to R\) this operator is an algebra homomorphism. This fact is used to derive, among others, the Newton identities relating the elementary invariants and the sum-of- powers invariants of endomorphisms A in End V.
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 16D80
zbMATH DE Number: 3977211
zbMATH Keywords: exterior power
zbMATH Keywords: direct sum
zbMATH Keywords: trace
zbMATH Keywords: algebra homomorphism
zbMATH Keywords: Newton identities
zbMATH Keywords: invariants
zbMATH Keywords: endomorphisms
reviewed by: Jens Schwaiger
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3977211