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A normal integral basis theorem. (English) Zbl 0345.12001


MSC:

11R04 Algebraic numbers; rings of algebraic integers
11R32 Galois theory
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References:

[1] Fröhlich, A., Artin root numbers and normal integral bases for quaternion fields, Invent. Math., 17, 143-166 (1972) · Zbl 0261.12008
[2] Fröhlich, A., Module invariants and roots numbers for quaternion fields of degree \(4l^r\), (Proc. Cambridge Philos. Soc., 76 (1974)), 393-399 · Zbl 0304.12008
[3] Fröhlich, A., Locally free modules over arithmetic orders, Crelle, 274/75, 112-138 (1975) · Zbl 0316.12013
[4] Fröhlich, A., Resolvents and trace form, (Math. Proc. Cambridge Philos. Soc., 8 (1975)), 85-210 · Zbl 0321.12019
[5] A. FröhlichCrelle; A. FröhlichCrelle
[6] Fröhlich, A.; Keating, M.; Wilson, S., The classgroups of dihedral 2-groups, Mathematika, 21, 64-71 (1974) · Zbl 0303.12006
[7] Galovich, A.; Reiner, I.; Ullom, S., Classgroups for integral representations of metacyclic groups, Mathematika, 19, 105-111 (1972) · Zbl 0248.12010
[8] Hasse, H., Artinsche Führer, Artinsche \(L\)-Funktionen und Gaussche Summen über endlich algebraischen Zahlkörpern, Acta Salmant. (1954) · Zbl 0057.27305
[9] Jacobinski, H., Genera and decomposition of lattices over orders, Acta Math., 121, 1-29 (1968) · Zbl 0167.04503
[10] Martinet, J., Sur l’arithmétique des extensions Galoisiennes a groupe de Galois diedral d’ordre \(2p\), Ann. Inst. Fourier, 19, 1-80 (1969) · Zbl 0165.06502
[11] Martinet, J., Modules sur l’algèbre du groupe quaternionien, Ann. Sci. École Norm. Sup., 4, 399-408 (1971) · Zbl 0219.12012
[12] Noether, E., Normalbasis bei Körpern ohne höhere Verzweigung, Crelle, 167, 147-152 (1932) · JFM 58.0172.02
[13] Reiner, I.; Ullom, S.; Mayer, A., Vietories sequence for classgroups, J. of Algebra, 31, 305-342 (1974)
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