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.
@article{bwmeta1.element.bwnjournal-article-cmv83i1p43bwm,
author = {Y. Hatzaras and Th. Theohari-Apostolidi},
title = {Hermitian and quadratic forms over local classical crossed product orders},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {43-53},
zbl = {0959.16016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p43bwm}
}
Hatzaras, Y.; Theohari-Apostolidi, Th. Hermitian and quadratic forms over local classical crossed product orders. Colloquium Mathematicae, Tome 84/85 (2000) pp. 43-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p43bwm/
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