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

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.


11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers


Zbl 0219.12012
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