Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T07:09:38.655Z Has data issue: false hasContentIssue false
  • English
  • Français

On the module structure of the ring of all integers of a p-adic number field

Published online by Cambridge University Press:  22 January 2016

Yoshimasa Miyata
Yoshimasa Miyata*
Affiliation:
Faculty of Education, Shizuoka University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let k be a p-adic number field and o be the ring of all integers of k. Let K/k be a cyclic ramified extension of prime degree p with Galois group G. Then the ring of all integers of K is o[G]-module. The purpose of this paper is to give a necessary and sufficient condition for o[G]-modale to be indecomposable.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 54 , July 1974 , pp. 53 - 59
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Artin, E. and Tate, J., Class Field Theory, Benjamin, New York, 1967.Google Scholar
[2] Amano, S., Eisenstein equations of degree p in a p-adic field, J. Fac. Sci. Univ. Tokyo vol. 18, No 1 (1971), 1–21.Google Scholar
[3] Bourbaki, N., Èléments de Mathématique Algèbre Chap. 4 et 5, Hermann, Paris, 1959.Google Scholar
[4] Maus, E., Arithmetisch disjunkte Körper, J. reine angew. Math. 226 (1967), 184–203.Google Scholar
[5] Jiten, Sügaku (Mathematical dictonary), Iwanami, Tokyo, 1968.Google Scholar