On lattices over valuation rings of arbitrary rank

Shaul Zemel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageAmerican English
Pages (from-to)812-852
Number of pages41
JournalJournal of Algebra
Volume423
DOIs
StatePublished - 1 Feb 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

  • Bilinear forms
  • Lattices
  • Valuation rings

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