منابع مشابه
On Multivariate Hermitian Quadratic Forms
Quantifier elimination over real closed fields (real QE) is an important area of research for various fields of mathematics and computer science. Though the cylindrical algebraic decomposition (CAD) algorithm introduced by G. E. Collins [4] and improved by many successive works has been considered as the most efficient method for a general real QE problem up to the present date, we may have a m...
متن کاملA Note on Hermitian Forms
In this note we effect a reduction of the theory of hermitian forms of two particular types (coefficients in a quadratic field or in a quaternion algebra with the usual anti-automorphism) to that of quadratic forms. The main theorem (§2) enables us to apply directly the known results on quadratic forms. This is illustrated in the discussion in §3 of a number of special cases. Let <£ be an arbit...
متن کاملSignatures of Hermitian Forms
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 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.
متن کاملOn hermitian trace forms over hilbertian fields
Let k be a field of characteristic different from 2. Let E/k be a finite separable extension with a k-linear involution σ. For every σ-symmetric element μ ∈ E∗, we define a hermitian scaled trace form by x ∈ E 7→ TrE/k(μxx). If μ = 1, it is called a hermitian trace form. In the following, we show that every even-dimensional quadratic form over a hilbertian field, which is not isomorphic to the ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1979
ISSN: 0021-8693
DOI: 10.1016/0021-8693(79)90168-6