# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Hermitian and quadratic forms over local classical crossed product orders

### Tom 83 / 2000

Colloquium Mathematicum 83 (2000), 43-53 DOI: 10.4064/cm-83-1-43-53

#### Streszczenie

Let R be a complete discrete valuation ring with quotient field K, L/K be a Galois extension with Galois group G and S be the integral closure of R in L. If a is a factor set of G with values in the group of units of S, then (L/K,a) (resp. Λ =(S/R,a)) denotes the crossed product K-algebra (resp. crossed product R -order in A). In this paper hermitian and quadratic forms on Λ -lattices are studied and the existence of at most two irreducible non-singular quadratic Λ -lattices is proved (Theorem 3.5). Further the orthogonal decomposition of an arbitrary non-singular quadratic Λ -lattice is given.

#### Autorzy

• Y. Hatzaras
• Th. Theohari-Apostolidi

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