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ArticleOriginal scientific text

Title

Hermitian and quadratic forms over local classical crossed product orders

Authors 1, 2

Affiliations

  1. Department of Civil Engineering, University of Thessaly, Pedion Areos, Volos 383 34, Greece
  2. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54 006, Greece

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.

Keywords

ENG
crossed-product order, quadratic form

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Colloquium Mathematicum
2000/83/1
Export to PBN, Opens in new tab
Pages:
43-53
Main language of publication
English
Received
1998-11-10
Accepted
1999-08-04
Published
2000
Exact and natural sciences