Elements of finite order in \(K_ 2\) of fields
type: Item
instance of: scholarly article
title: Elements of finite order in \(K_ 2\) of fields
zbMATH Open document ID: 0815.11056
author: Hourong Qin
published in: Chinese Science Bulletin
publication date: 1994-10-24T00:00:00Z
review text: The author proves two results concerning the Milnor symbol \(\{a,b\}\) in \(K_ 2 (F)\), \(F\) a field. (i) If the characteristic of \(F\) is not 2, then every element of order 4 in \(K_ 2 (F)\) has the form \(\{a, a^ 2 + 1\} \{-1, b\}\), where \(a\), \(a^ 2 + 1\) and \(b\) are all nonzero elements of \(F\). (It is known that the second factor is a typical element of order 2.) (ii) The subset \(\{a, \Phi_{2^ n} (a)\}\) of \(K_ 2 (\mathbb{Q})\), \(\Phi_{2^ n}\) a cyclotomic polynomial, is a subgroup only for \(n = 1,2\).
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 19C20
zbMATH DE Number: 640472
zbMATH Keywords: elements of finite order
zbMATH Keywords: \(K\)-theory of fields
zbMATH Keywords: \(K_ 2\)
zbMATH Keywords: Milnor symbol
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 640472