Cougnard, Jean Construction of a normal basis for extensions of \(\mathbb Q\) with group \(D_4\). (Construction de base normale pour les extensions de \(\mathbb Q\) à groupe \(D_4\).) (French) Zbl 1161.11397 J. Théor. Nombres Bordx. 12, No. 2, 399-409 (2000). Summary: In a paper published in 1971 [Ann. Sci. Éc. Norm. Supér. (4) 4, 399–408 (1971; Zbl 0219.12012)], mainly devoted to quaternionian extensions, J. Martinet proved the existence of normal integral bases for tame \(D_4\) extensions of \(\mathbb Q\). We give a constructive proof of this result. Cited in 3 Documents MSC: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers Citations:Zbl 0219.12012 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] Cougnard, J., Anneau d’entiers stablement libre sur Z[H8 x C2]. J. Théor. Nombres Bordeaux10 (1998), 163-201. · Zbl 0924.11093 [2] Hilbert, D., Die Theorie der algebraischen Zahlkörper (Zahlbericht). Jahr. Ber. der deutschen Math. Ver.4 (1897), 175-146, ou Gesammelte Abhandlungen, 63-363. · JFM 28.0157.05 [3] Martinet, J., Sur l’arithmétique d’une extension galoisienne à groupe de Galois diédral d’ordre 2p. Ann. Inst. Fourier19 (1969), 1-80. · Zbl 0165.06502 [4] Martinet, J., Modules sur l’algèbre du groupe quaternionien. Annales Sci. de l’Ec. normale sup. (4) 3 (1971), 399-408. · Zbl 0219.12012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.