\(K_ 2\) d'un anneau euclidien
type: Item
instance of: scholarly article
title: \(K_ 2\) d'un anneau euclidien
zbMATH Open document ID: 0552.18002
DOI: 10.1016/0022-4049(84)90038-0
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: Let A be a Dedekind domain with field of fractions F. The map \(K_ 2(A)\to K_ 2(F)\) is known to be injective when the residue fields of A are algebraic over a finite field, when A is a discrete valuation ring, or when A is the polynomial ring in one variable over a field. In this note the author shows that \(K_ 2(A)\to K_ 2(F)\) is injective whenever A is Euclidean. His argument is based on a lifting trick inspired by the Tate-Gauss computation of \(K_ 2{\mathbb{Q}}\).
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 13D15
Mathematics Subject Classification ID: 13F07
zbMATH DE Number: 3879118
zbMATH Keywords: algebraic K-theory
zbMATH Keywords: \(K_ 2\)
zbMATH Keywords: Euclidean ring
zbMATH Keywords: Dedekind domain
author: Bruno Kahn
reviewed by: Michael R. Stein
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90038-0
OpenAlex ID: W1983005385
cites work: Higher algebraic K-theory: I
cites work: \(K_2\) of discrete valuation rings
cites work: Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
cites work: Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
cites work: Q5562621
cites work: Q3943047
description: scientific article; zbMATH DE number 3879118