# Hermitian and quadratic forms over local classical crossed product orders

Colloquium Mathematicae (2000)

• Volume: 83, Issue: 1, page 43-53
• ISSN: 0010-1354

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## Abstract

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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.

## How to cite

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Hatzaras, Y., and Theohari-Apostolidi, Th.. "Hermitian and quadratic forms over local classical crossed product orders." Colloquium Mathematicae 83.1 (2000): 43-53. <http://eudml.org/doc/210772>.

@article{Hatzaras2000,
abstract = {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.},
author = {Hatzaras, Y., Theohari-Apostolidi, Th.},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {43-53},
title = {Hermitian and quadratic forms over local classical crossed product orders},
url = {http://eudml.org/doc/210772},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Hatzaras, Y.
AU - Theohari-Apostolidi, Th.
TI - Hermitian and quadratic forms over local classical crossed product orders
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 43
EP - 53
AB - 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.
LA - eng
UR - http://eudml.org/doc/210772
ER -

## References

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