Gorenstein Witt rings. (English) Zbl 0655.13026
We study the structure of Noetherian Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). For 1-dimensional Witt rings R, R is Gorenstein iff R is a group ring over \({\mathbb{Z}}\). A number of striking properties are shown to hold for 0-dimensional Gorenstein Witt rings, such as \(ann(ann(I))=I\) for any ideal I. Under an additional assumption on annihilators we show that Gorenstein Witt rings are group ring extensions of Witt rings of local type.
Reviewer: R.W.Fitzgerald
MSC:
13H10 | Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) |
11E16 | General binary quadratic forms |