Annihilators of quadratic and bilinear forms over fields of characteristic two
نویسندگان
چکیده
منابع مشابه
Symmetric bilinear forms over finite fields of even characteristic
Let Sm be the set of symmetric bilinear forms on an m-dimensional vector space over GF(q), where q is a power of two. A subset Y of Sm is called an (m, d)-set if the difference of every two distinct elements in Y has rank at least d. Such objects are closely related to certain families of codes over Galois rings of characteristic four. An upper bound on the size of (m, d)-sets is derived, and i...
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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...
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This paper is intended to give a survey in the algebraic theory of quadratic forms over fields of characteristic two. The relationship between differential forms and quadratics and bilinear forms over such fields discovered by Kato is used to reduced some problems on quadratics forms to concrete questions about differential forms, which in general are easier to handle. 1991 Mathematics Subject ...
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Introduction. Witt [5] proved that two binary or ternary quadratic forms, over an arbitrary field (of characteristic not 2) are equivalent if and only if they have the same determinant and Hasse invariant. His proof is brief and elegant but uses a lot of the theory of simple algebras. The purpose of this note is to make this fundamental theorem more accessible by giving a short proof using only...
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1. The Hasse Principle(s) For Quadratic Forms Over Global Fields 1 1.1. Reminders on global fields 1 1.2. Statement of the Hasse Principles 2 2. The Hasse Principle Over Q 3 2.1. Preliminary Results: Reciprocity and Approximation 3 2.2. n ≤ 1 6 2.3. n = 2 6 2.4. n = 3 6 2.5. n = 4 8 2.6. n ≥ 5 9 3. The Hasse Principle Over a Global Field 9 3.1. n = 2 10 3.2. n = 3 10 3.3. n = 4 11 3.4. n ≥ 5 12...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.10.040