منابع مشابه
Cohomological Invariants of Quaternionic Skew-hermitian Forms
We define a complete system of invariants en,Q, n ≥ 0 for quaternionic skew-hermitian forms, which are twisted versions of the invariants en for quadratic forms. We also show that quaternionic skew-hermitian forms defined over a field of 2-cohomological dimension at most 3 are classified by rank, discriminant, Clifford invariant and Rost invariant.
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Signatures of quadratic forms over formally real fields have been generalized in [BP2] to hermitian forms over central simple algebras with involution over such fields. This was achieved by means of an application of Morita theory and a reduction to the quadratic form case. A priori, signatures of hermitian forms can only be defined up to sign, i.e., a canonical definition of signature is not p...
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We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author’s previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation ξΦ · ξ = Ψ , where Φ and Ψ represent he...
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We will determine (up to equivalence) all of the integral positive definite Hermitian lattices in imaginary quadratic fields of class number 1 that represent all positive integers.
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Let D be a division ring with an involution. Assuming that D admits Baer orderings, we can study the Witt group of hermitian froms over D by observing its image in the ring of continuous functions on the space of orderings. We are led to define a new class of rings which, when viewed in an abstract setting, provide a natural generalization of the spaces of orderings and real spectra studied in ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90245-8