A note on Witt rings of 2-fold full rings. (English) Zbl 0587.13004

Cho, In-Ho; Kim, Jae-Gyeom

Bull. Korean Math. Soc. 22, 121-126 (1985).

The main theorem is that when R and S are 2-fold full, the Witt rings W(R) and W(S) are isomorphic if and only if \(W(R)/I(R)^ 3\) and \(W(S)/I(S)^ 3\) are isomorphic, where I(R) and I(S) are the fundamental ideals of W(R) and W(S) respectively. The analogous results for the cases when R and S are fields, or semi-local rings with 2 invertible, are due to D. K. Harrison; cf. J. K. Arason and A. Pfister [Invent. Math. 12, 173-176 (1971; Zbl 0212.373)] and K. I. Mandelberg [Can. J. Math. 27, 513-527 (1975; Zbl 0273.13017)].

Reviewer: C.Small

MSC:

13C05	Structure, classification theorems for modules and ideals in commutative rings
11E16	General binary quadratic forms

Keywords:

2-fold full rings; Witt ring of commutative ring; quadratic forms