Relative Galois module structure of integers of local abelian fields

Günter Lettl

Acta Arithmetica (1998)

  • Volume: 85, Issue: 3, page 235-248
  • ISSN: 0065-1036

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Günter Lettl. "Relative Galois module structure of integers of local abelian fields." Acta Arithmetica 85.3 (1998): 235-248. <http://eudml.org/doc/207166>.

@article{GünterLettl1998,
author = {Günter Lettl},
journal = {Acta Arithmetica},
keywords = {associated orders; normal basis; ramification},
language = {eng},
number = {3},
pages = {235-248},
title = {Relative Galois module structure of integers of local abelian fields},
url = {http://eudml.org/doc/207166},
volume = {85},
year = {1998},
}

TY - JOUR
AU - Günter Lettl
TI - Relative Galois module structure of integers of local abelian fields
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 3
SP - 235
EP - 248
LA - eng
KW - associated orders; normal basis; ramification
UR - http://eudml.org/doc/207166
ER -

References

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  1. [1] F. Bertrandias et M.-J. Ferton, Sur l'anneau des entiers d'une extension cyclique de degré premier d'un corps local, C. R. Acad. Sci. Paris Sér. A 274 (1972), 1330-1333. Zbl0235.12007
  2. [2] W. Bley, A Leopoldt-type result for rings of integers of cyclotomic extensions, Canad. Math. Bull. 38 (1995), 141-148. Zbl0830.11037
  3. [3] J. Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157-166. Zbl0609.12009
  4. [4] N. P. Byott, Galois structure of ideals in wildly ramified abelian p-extensions of a p-adic field, and some applications, J. Théor. Nombres Bordeaux 9 (1997), 201-219. Zbl0889.11040
  5. [5] N. P. Byott and G. Lettl, Relative Galois module structure of integers of abelian fields, ibid. 8 (1996), 125-141. Zbl0859.11059
  6. [6] S.-P. Chan and C.-H. Lim, Relative Galois module structure of rings of integers of cyclotomic fields, J. Reine Angew. Math. 434 (1993), 205-220. Zbl0753.11038
  7. [7] L. Childs, Taming wild extensions with Hopf algebras, Trans. Amer. Math. Soc. 304 (1987), 111-140. Zbl0632.12013
  8. [8] L. Childs and D. J. Moss, Hopf algebras and local Galois module theory, in: Advances in Hopf Algebras, J. Bergen and S. Montgomery (eds.), Lecture Notes in Pure and Appl. Math. 158, Dekker, Basel, 1994, 1-24. Zbl0826.16035
  9. [9] C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. I, Pure Appl. Math., Wiley, 1981. 
  10. [10] A. Fröhlich, Invariants for modules over commutative separable orders, Quart. J. Math. Oxford Ser. (2) 16 (1965), 193-232. Zbl0192.14002
  11. [11] A. Fröhlich, Galois module structure of algebraic integers, Ergeb. Math. Grenzgeb. 3, Vol. 1, Springer, 1983. Zbl0501.12012
  12. [12] H.-W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959), 119-149. Zbl0098.03403
  13. [13] G. Lettl, The ring of integers of an abelian number field, ibid. 404 (1990), 162-170. Zbl0703.11060
  14. [14] G. Lettl, Note on the Galois module structure of quadratic extensions, Colloq. Math. 67 (1994), 15-19. Zbl0812.11063
  15. [15] I. Reiner, Maximal Orders, London Math. Soc. Monographs 5, Academic Press, 1975. 
  16. [16] K. W. Roggenkamp and M. J. Taylor, Group rings and class groups, DMV-Sem. 18, Birkhäuser, 1992. 
  17. [17] M. J. Taylor, On the Galois module structure of rings of integers of wild, abelian extensions, J. London Math. Soc. 52 (1995), 73-87. Zbl0857.11059

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