Quadratic forms and Linkage of Quaternion Algebras

1988 ◽  
Vol 31 (3) ◽  
pp. 301-307
Author(s):  
Vatsala Krishnamani ◽  
Joseph Yucas
Keyword(s):  
Quadratic Forms ◽  
Strong Approximation ◽  
Approximation Property ◽  
Quaternion Algebras ◽  
Torsion Freeness

AbstractA field F satisfies n-linkage on a subset of Ḟ if whenever the quaternion algebrasare equal in Br(F) there exist z ∈ Ḟ withfor i = 1, 2, . . ., n. This linkage of quaternion algebras is examined and its relationship to the torsion freeness of I2(F) and to the strong approximation property is investigated.

scholarly journals Transfer of quadratic forms and of quaternion algebras over quadratic field extensions

2018 ◽  
Vol 111 (2) ◽  
pp. 135-143
Author(s):  
Karim Johannes Becher ◽  
Nicolas Grenier-Boley ◽  
Jean-Pierre Tignol
Keyword(s):  
Quadratic Forms ◽  
Quadratic Field ◽  
Quaternion Algebras ◽  
Field Extensions

27.—Generating Sets for Fuchsian Groups

1975 ◽  
Vol 72 (4) ◽  
pp. 317-326 ◽  
Author(s):  
J. H. H. Chalk ◽  
B. G. A. Kelly
Keyword(s):  
Quadratic Forms ◽  
Fundamental Region ◽  
Fuchsian Groups ◽  
Quaternion Algebras ◽  
Generating Sets ◽  
Complete Set ◽  
Explicit Bounds

SynopsisFor a class of Fuchsian groups, which includes integral automorphs of quadratic forms and unit groups of indefinite quaternion algebras, it is shown that the geometry of a suitably chosen fundamental region leads to explicit bounds for a complete set of generators.

scholarly journals Strong approximation of quadrics and representations of quadratic forms

2008 ◽  
Vol 128 (7) ◽  
pp. 2091-2096
Author(s):  
Constantin N. Beli ◽  
Wai Kiu Chan
Keyword(s):  
Quadratic Forms ◽  
Strong Approximation

scholarly journals History, Developments and Open Problems on Approximation Properties

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1117
Author(s):  
Ju Myung Kim ◽  
Bentuo Zheng
Keyword(s):  
Recent Progress ◽  
Strong Approximation ◽  
Approximation Property ◽  
Approximation Properties ◽  
Open Problems ◽  
Comprehensive Review ◽  
Classical Approximation

In this paper, we give a comprehensive review of the classical approximation property. Then, we present some important results on modern variants, such as the weak bounded approximation property, the strong approximation property and p-approximation property. Most recent progress on E-approximation property and open problems are discussed at the end.

scholarly journals Addendum: "Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras"

2015 ◽  
Vol 14 (07) ◽  
pp. 1591001
Author(s):  
Adam Chapman
Keyword(s):  
Quadratic Forms ◽  
Tensor Products ◽  
Quaternion Algebras

We show how the chain lemma for quaternion algebras over fields of F ≠ 2 and [Formula: see text] can be strengthened so that up to two slots are changed at a time.

scholarly journals Optimal strong approximation for quadratic forms

2019 ◽  
Vol 168 (10) ◽  
pp. 1887-1927 ◽  
Author(s):  
Naser T. Sardari
Keyword(s):  
Quadratic Forms ◽  
Strong Approximation
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