Combinatorial techniques and abstract Witt rings III

Robert Fitzgerald

Vol. 148 (1991), No. 1, 39–58

DOI: 10.2140/pjm.1991.148.39

Abstract

We introduce an equivalence relation on maximal elements (i.e., D⟨1,−x⟩ is maximal). We present a form theoretic proof of Marshall’s classification of reduced Witt rings, thus providing a possible outline for proving the full elementary type conjecture. The same relation restricted to elements of index two yields characterizations of Witt rings with a factor either of local type or a group ring extension of a totally degenerate Witt ring.

Mathematical Subject Classification 2000

Primary: 11E81

Secondary: 19G12

Milestones

Received: 30 September 1988

Revised: 18 January 1990

Published: 1 March 1991