Generalized rigid elements in fields

Kazimierz Szymiczek

Vol. 129 (1987), No. 1, 171–186

DOI: 10.2140/pjm.1987.129.171

Abstract

Rigid elements in a field, should they exist, have strong influence on structure of the Witt ring of the field. We generalize rigid elements to the context of n-fold Pfister forms in two ways and study the relations between n-rigid and super n-rigid elements in various classes of fields including global fields, and in abstract Witt rings. In special cases the existence of higher rigidities turns out to be equivalent to important properties of fields known in literature. Among these are the property A_n, torsion freeness of IⁿF and finite stability index of WF.

Mathematical Subject Classification 2000

Primary: 11E81

Secondary: 11E04, 19G12

Milestones

Received: 16 May 1985

Revised: 19 September 1986

Published: 1 September 1987