ℚ-adequacy of Galois 2-extensions

Helen G. Grundman; David B. Leep; Tara L. Smith

doi:10.1007/BF02764068

ℚ-adequacy of Galois 2-extensions

Helen G. Grundman, David B. Leep, Tara L. Smith

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The ℚ-adequacy of any finite Galois 2-extension of ℚ is shown to depend only on the ℚ-adequacy of its maximal elementary abelian intermediate field, which must be either quadratic (and hence always ℚ-adequate) or biquadratic over ℚ. A precise description of those biquadratic extensions of ℚ which are ℚ-adequate is given. This then gives a method for explicitly determining whether any given finite Galois 2-extension of ℚ can arise as a subfield of a ℚ-central division algebra.

Original language	English
Pages (from-to)	11-19
Number of pages	9
Journal	Israel Journal of Mathematics
Volume	130
DOIs	https://doi.org/10.1007/BF02764068
State	Published - 2002

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/BF02764068

Cite this

@article{247f5990899e435a94c9e87b3e9066a4,

title = "ℚ-adequacy of Galois 2-extensions",

abstract = "The ℚ-adequacy of any finite Galois 2-extension of ℚ is shown to depend only on the ℚ-adequacy of its maximal elementary abelian intermediate field, which must be either quadratic (and hence always ℚ-adequate) or biquadratic over ℚ. A precise description of those biquadratic extensions of ℚ which are ℚ-adequate is given. This then gives a method for explicitly determining whether any given finite Galois 2-extension of ℚ can arise as a subfield of a ℚ-central division algebra.",

author = "Grundman, {Helen G.} and Leep, {David B.} and Smith, {Tara L.}",

year = "2002",

doi = "10.1007/BF02764068",

language = "English",

volume = "130",

pages = "11--19",

}

TY - JOUR

T1 - ℚ-adequacy of Galois 2-extensions

AU - Grundman, Helen G.

AU - Leep, David B.

AU - Smith, Tara L.

PY - 2002

Y1 - 2002

N2 - The ℚ-adequacy of any finite Galois 2-extension of ℚ is shown to depend only on the ℚ-adequacy of its maximal elementary abelian intermediate field, which must be either quadratic (and hence always ℚ-adequate) or biquadratic over ℚ. A precise description of those biquadratic extensions of ℚ which are ℚ-adequate is given. This then gives a method for explicitly determining whether any given finite Galois 2-extension of ℚ can arise as a subfield of a ℚ-central division algebra.

AB - The ℚ-adequacy of any finite Galois 2-extension of ℚ is shown to depend only on the ℚ-adequacy of its maximal elementary abelian intermediate field, which must be either quadratic (and hence always ℚ-adequate) or biquadratic over ℚ. A precise description of those biquadratic extensions of ℚ which are ℚ-adequate is given. This then gives a method for explicitly determining whether any given finite Galois 2-extension of ℚ can arise as a subfield of a ℚ-central division algebra.

UR - http://www.scopus.com/inward/record.url?scp=0036353531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036353531&partnerID=8YFLogxK

U2 - 10.1007/BF02764068

DO - 10.1007/BF02764068

M3 - Article

AN - SCOPUS:0036353531

SN - 0021-2172

VL - 130

SP - 11

EP - 19

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

ℚ-adequacy of Galois 2-extensions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this