Quotients of Milnor K-rings, orderings, and valuations

Ido Efrat

Vol. 226 (2006), No. 2, 259–275

DOI: 10.2140/pjm.2006.226.259

Abstract

We define and study the Milnor K-ring of a field F modulo a subgroup of the multiplicative group of F. We compute it in several arithmetical situations, and study the reflection of orderings and valuations in this ring.

Keywords

generalized Milnor K-rings, orderings, valuations

Mathematical Subject Classification 2000

Primary: 19F99

Secondary: 12J10, 12J15, 12E30

Milestones

Received: 29 August 2004

Revised: 14 January 2005

Accepted: 14 January 2005

Published: 1 August 2006