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arXiv · 1308.3108

On Lattices over Valuation Rings of Arbitrary Rank

Shaul Zemel
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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.

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Shaul Zemel. 2013-08-14. On Lattices over Valuation Rings of Arbitrary Rank. https://doi.org/10.1016/j.jalgebra.2014.10.022

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