On the classification of quadratic forms over semi local rings
نویسندگان
چکیده
منابع مشابه
The Artin-springer Theorem for Quadratic Forms over Semi-local Rings with Finite Residue Fields
Let R be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over R remain anisotropic after base change to any odd-degree finite étale extension of R. This generalization of the classical Artin-Springer theorem (concerning the situation where R is a field) was previously established in the case where all residue fields of R...
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real spectrum (ARS)finitely closed subset of, 52morphism of, 31projective limits of, 31residue space of, 66–69saturated subset of, 56subspace of, 61algebraLukasiewicz, 84Kleene, 87Post, 84AOSclosed subset, 210dependent subset, 210AOS-fan, 166archimedean-equivalent, 188ARS-fan, 170connected components, 208finiteisomorphi...
متن کاملAbsolute Stable Rank and Quadratic Forms over Noncommutative Rings
One o f the ma in aims o f [5] is to obta in bounds for asr(A) for var ious classes of noncommuta t i ve rings A; in part icular , they show that: (i) asr(A) ~< 1 + d whenever A is a module finite a lgebra over a commuta t ive Noe ther ian ring R with d im(maxspec R) = d, and (ii) asr(A) = 1 if A is a semi-local ring (see [5], Theorems 3.1 and 2.4], respectively). The a im o f this note is to s...
متن کاملClassification of Quadratic Forms over Skew Fields of Characteristic 2
Quadratic forms over division algebras over local or global fields of characteristic 2 are classified by an invariant derived from the Clifford algebra construction. Quadratic forms over skew fields were defined by Tits in [14] to investigate twisted forms of orthogonal groups in characteristic 2, and by C.T.C. Wall [16] in a topological context. The purpose of this paper is to obtain a classif...
متن کاملQuadratic and Symmetric Bilinear Compositions of Quadratic Forms over Commutative Rings
Over commutative rings in which 2 is a zero-divisor, to compose a quadratic form with symmetric bilinear forms or with quadratic forms is not quite the same. In this paper the relation between the two classes of compositions is clarified and the results applied to find the ranks of minimal compositions.
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ژورنال
عنوان ژورنال: Mémoires de la Société mathématique de France
سال: 1979
ISSN: 0249-633X,2275-3230
DOI: 10.24033/msmf.244