On lattices over valuation rings of arbitrary rank

JOURNAL OF ALGEBRA

卷:423

Article

Zemel, Shaul

关键词: Lattices;    Bilinear forms;    Valuation rings;   

DOI  :  10.1016/j.jalgebra.2014.10.022

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free