Extension of scalars in the corestriction of an algebra
type: Item
instance of: scholarly article
title: Extension of scalars in the corestriction of an algebra
zbMATH Open document ID: 0595.16013
DOI: 10.1016/0022-4049(86)90102-7
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: For algebras over fields the corestriction over finite separable field extensions is a very useful technique. Let A be an algebra over a field L, L/K a finite separable extension and E/K an arbitrary extension. Thus \(E\otimes_ KL=L_ 1\otimes...\otimes L_ s\). The author shows that \[ E\otimes_ KCor_{L/K}A=(Cor_{L_ 1/E}A_{L_ 1})\otimes_ E...\otimes_ E(Cor_{L_ s/E}A_{L_ s}) \] where \(A_{L_ i}=L_ i\otimes_ LA\). The special case where L/K is an extension of global fields, while E is the completion of K at a prime, yields that the \(L_ i\) are the completions of L at the primes lying over the prime of K. In a final section the author studies the integral analogue of these results and shows that when certain primes ramify the results do not carry over.
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 14E22
zbMATH DE Number: 3957351
zbMATH Keywords: corestriction
zbMATH Keywords: finite separable field extensions
zbMATH Keywords: extension of global fields
author: Carl R. Riehm
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90102-7
OpenAlex ID: W1987089471
cites work: Q5516858
cites work: Algèbre
cites work: Q3843687
cites work: Q3963168
cites work: The corestriction of algebraic structures
cites work: Corestriction of Orders
description: scientific article; zbMATH DE number 3957351