# Hermitian and quadratic forms over local classical crossed product orders

Y. Hatzaras; Th. Theohari-Apostolidi

Colloquium Mathematicae (2000)

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

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topHatzaras, 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},

keywords = {crossed-product order; quadratic form; crossed product orders; quadratic forms; quadratic lattices; Hermitean forms},

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

KW - crossed-product order; quadratic form; crossed product orders; quadratic forms; quadratic lattices; Hermitean forms

UR - http://eudml.org/doc/210772

ER -

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