On quaternion algebras over some extensions of quadratic number fields

被引：1

作者：

Acciaro, V ^{[1
]}

Savin, D. ^{[2
]}

Taous, M. ^{[3
]}

Zekhnini, A. ^{[4
]}

机构：

[1] Univ G dAnnunzio, Dipartimento Econ, Viale Pindaro 42, I-65127 Pescara, Italy

[2] Transilvania Univ Brasov, Fac Math & Comp Sci, Iuliu Maniu St 50, Brasov 500091, Romania

[3] Moulay Ismail Univ, Fac Sci & Technol, Dept Math, Errachidia, Morocco

[4] Mohammed Premier Univ, Sci Fac, Dept Math, Oujda, Morocco

来源：

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA | 2021年 / 27卷 / 03期

关键词：

Quaternion algebras; Quadratic fields; Dihedral extension; Hilbert class field;

D O I：

10.1007/s40590-021-00365-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p and q be two positive primes, let l be an odd positive prime and let F be a quadratic number field. Let K be an extension of F of degree l such that K is a dihedral extension of Q, or else let K be an abelian l-extension of F unramified over F whenever l divides the class number of F. In this paper, we provide a complete characterization of division quaternion algebras H-K(p, q) over K.

引用

页数：7

共 50 条

[21] Some explicit constructions of integral structures in quaternion algebras
Ciavarella, Miriam
Terracini, Lea
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (5-7) : 1013 - 1026
[22] Classes of order 4 in the strict class group of number fields and remarks on unramified quadratic extensions of unit type
Dummit, David S.
ANNALES MATHEMATIQUES DU QUEBEC, 2019, 43 (02): : 221 - 231
[23] Classes of order 4 in the strict class group of number fields and remarks on unramified quadratic extensions of unit type
David S. Dummit
Annales mathématiques du Québec, 2019, 43 : 221 - 231
[24] Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras
Chapman, Adam
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (03)
[25] Infinite 2-class field towers of some imaginary quadratic number fields
Sueyoshi, Y
ACTA ARITHMETICA, 2004, 113 (03) : 251 - 257
[26] Some rank records for elliptic curves with prescribed torsion over quadratic fields
Najman, Filip
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2014, 22 (01): : 215 - 219
[27] Siegel series for skew Hermitian forms over quaternion algebras
Shunsuke Yamana
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2017, 87 : 43 - 59
[28] Rank one sheaves over quaternion algebras on Enriques surfaces
Reede, Fabian
ADVANCES IN GEOMETRY, 2022, 22 (01) : 105 - 112
[29] Siegel series for skew Hermitian forms over quaternion algebras
Yamana, Shunsuke
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2017, 87 (01): : 43 - 59
[30] On a theorem of Scholz on the class number of quadratic fields
Nemenzo, FR
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2004, 80 (02) : 9 - 11

← 1 2 3 4 5 →