Combinatorial techniques and abstract Witt rings. III (Q1263611)

[For part I cf. the author and \textit{J. Yucas}, J. Algebra 114, No.1, 40- 52 (1988; Zbl 0641.10018).] 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.