English

On Lattices over Valuation Rings of Arbitrary Rank

Commutative Algebra 2020-08-12 v2

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 polynomial. If 2 is invertible we obtain the uniqueness of the Jordan decomposition and the Witt Cancelation 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.

Keywords

Cite

@article{arxiv.1308.3108,
  title  = {On Lattices over Valuation Rings of Arbitrary Rank},
  author = {Shaul Zemel},
  journal= {arXiv preprint arXiv:1308.3108},
  year   = {2020}
}

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30 pages