Niveau hermitien de Certaines algèbres de quaternions

Serhir, Ahmed

doi:10.1080/00927879708826003

Cited by 3 publications

(2 citation statements)

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“…This result holds for a ®eld with trivial or non-trivial involution, and quaternion division algebras with involution of ®rst kind [6,5,9] . This result holds for a ®eld with trivial or non-trivial involution, and quaternion division algebras with involution of ®rst kind [6,5,9] .…”

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confidence: 65%

Niveau Hermitien d'UNE Algèbre De Quaternions À Division Munie d'UNE Involution De Deuxième Espèce

Serhir

2002

Communications in Algebra

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confidence: 65%

Niveau Hermitien d'UNE Algèbre De Quaternions À Division Munie d'UNE Involution De Deuxième Espèce

Serhir

2002

Communications in Algebra

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“…We investigate the hermitian level of composition algebras C with involution over a ring R, extending the results of Lewis [7] for the standard involution and some of the results of Serhir [14] for the non-standard involution on C (which we introduce here in a more general context). In particular, we show that over semilocal rings where 2 is invertible, the hermitian level of (C, ) is a power of two if it is finite and that all powers of two can occur as the hermitian level of (C, ).…”

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confidence: 99%

The hermitian level of composition algebras

Pumplün

Unger

2002

manuscripta mathematica

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Abstract. The hermitian level of composition algebras with involution over a ring is studied. In particular, it is shown that the hermitian level of a composition algebra with standard involution over a semilocal ring, where two is invertible, is always a power of two when finite. Furthermore, any power of two can occur as the hermitian level of a composition algebra with nonstandard involution. Some bounds are obtained for the hermitian level of a composition algebra with involution of the second kind.

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On Hermitian Pfister Forms

Grenier-Boley¹,

Lequeu

Mahmoudi

2008

J. Algebra Appl.

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Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamental ideal of the Witt ring of K is lower bounded. In this paper, weak analogues of these two statements are proved for hermitian forms over a multiquaternion algebra with involution. Consequences for Pfister involutions are also drawn. An invariant uα of K with respect to a non-zero pure quaternion of a quaternion division algebra over K is defined. Upper bounds for this invariant are provided. In particular an analogue is obtained of a result of Elman and Lam concerning the u-invariant of a field of level at most 2.

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Niveau hermitien de Certaines algèbres de quaternions

Cited by 3 publications

References 5 publications

Niveau Hermitien d'UNE Algèbre De Quaternions À Division Munie d'UNE Involution De Deuxième Espèce

Niveau Hermitien d'UNE Algèbre De Quaternions À Division Munie d'UNE Involution De Deuxième Espèce

The hermitian level of composition algebras

On Hermitian Pfister Forms

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