Module structure of rings of integers in octahedral extensions

Acta Arithmetica

Volumn 109, Issue 4, 2003, Pages 321-327

  Godin, M ^a   Sodaigui B ^a  

^a UNIVERSITÉ DE VALENCIENNES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042363502     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa109-4-2     Document Type: Article

References (17)

1. [A] E. Artin, Questions de base minimale dans la théorie des nombres algébriques, in: Colloq, Internat. CNRS 24, Paris, 1950, 19-20.
2. 3, Colloq. Math. 71 (1996), 297-303.
3. [C2] _, Module structure of integers in metacyclic extensions, ibid. 76 (1998), 191-199.
4. 3, Acta Arith. 78 (1997), 297-303.
5. [E] L. P. Endo, Steinitz classes of tamely ramified Galois extensions of algebraic number fields, thesis, University of Illinois at Urbana-Champaign, 1975.
6. [F] A. Fröhlich, The discriminant of relative extensions and the existence of integral bases, Mathematika 7 (1960), 15-22.
7. [FT] A. Fröhlich and M. J. Taylor, Algebraic Number Theory, Cambridge Univ. Press, 1991.
8. 4, J. Théor. Nombres Bordeaux 14 (2002), 241-248.
9. [H] E. Hecke, Lectures on the Theory of Algebraic Numbers, Grad. Texts in Math. 77, Springer, New York, 1981.
10. 4, Acta Arith. 69 (1995), 259-276.
11. [Ma] J. Martinet, Discriminants and permutation groups, in: Number Theory, R. A. Molin (ed.), de Gruyter, Berlin, 1990, 359-385.
12. [Mc] L. R. McCulloh, Galois module structure of abelian extensions, J. Reine Angew. Math. 375/376 (1987), 259-306.
13. [N] J. Neukirch, Class Field Theory, Springer, Berlin, 1986.
14. [So1] B. Sodaïgui, Classes de Steinitz d'extensions galoisiennes relatives de degré une puissance de 2 et problème de plongement, Illinois J. Math. 43 (1999), 47-60.
15. [So2] _, Relative Galois module structure and Steinitz classes of dihedral extensions of degree 8, J. Algebra 223 (1999), 367-378.
16. [So3] _, Realizable classes of quaternion extensions of degree 41, J. Number Theory 80 (2000), 304-315.
17. [W] L. C. Washington, Introduction to Cyclotomic Fields, 2nd ed., Springer, Berlin. 1996.