On skew field coproducts with a finite extension
type: Item
instance of: scholarly article
title: On skew field coproducts with a finite extension
zbMATH Open document ID: 0888.16013
DOI: 10.1007/BF02785539
published in: Israel Journal of Mathematics
publication date: 1998-03-11T00:00:00Z
review text: The author considers one of the most interesting constructions in skew field theory (which was introduced by him many years ago), namely the skew field coproduct. In this paper he looks at the skew field coproduct \(U\) of a skew field \(E\) which is a \(k\)-algebra with a commutative binomial extension \(F\) of \(k\), i.e. an extension given by a polynomial \(x^n-\lambda\). He shows that \(U\) can be expressed as a cyclic extension of the skew field coproduct \(K\) of \([F:k]\) copies of \(E\). As a linear space \(U\) can be also viewed as a tensor product of \(K\) with \(F\) but with more complicated multiplication. He also provides additional information on the centralizer of \(F\) in \(U\) and examines the case when \(F\) is a Galois extension.
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 16K40
zbMATH DE Number: 997621
zbMATH Keywords: skew field coproducts
zbMATH Keywords: binomial extensions
zbMATH Keywords: cyclic extensions
zbMATH Keywords: tensor products
zbMATH Keywords: centralizers
zbMATH Keywords: Galois extensions
author: Paul M. Cohn
reviewed by: Leonid Makar-Limanov
MaRDI profile type: Publication
cites work: Q3808246
cites work: Q4692705
cites work: Q4848757
cites work: The Universal Field of Fractions of a Semifir: III. Centralizers and Normalizers
full work available at URL: https://doi.org/10.1007/bf02785539
OpenAlex ID: W2044109388
description: scientific article; zbMATH DE number 997621