Abstract
We show how several results about p-adic lattices generalize easily to lattices over valuation ring of arbitrary rank having only the Henselian property for quadratic polynomials. If 2 is invertible we obtain the uniqueness of the Jordan decomposition and the Witt Cancellation Theorem. We show that the isomorphism classes of indecomposable rank 2 lattices over such a ring in which 2 is not invertible are characterized by two invariants, provided that the lattices contain a primitive norm divisible by 2 of maximal valuation.
| Original language | English |
|---|---|
| Pages (from-to) | 812-852 |
| Number of pages | 41 |
| Journal | Journal of Algebra |
| Volume | 423 |
| DOIs | |
| State | Published - 1 Feb 2015 |
| Externally published | Yes |
Keywords
- Bilinear forms
- Lattices
- Valuation rings
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory