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On the module structure in a cyclic extension over a -adic number field

Published online by Cambridge University Press:  22 January 2016

Yoshimasa Miyata
Yoshimasa Miyata*
Affiliation:
Faculty of Education, Shizuoka University
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Let p be a prime. Let k be a -adic number field and be the ring of all integers of k. Let K/k be a cyclic totally ramified extension of degree pn with Galois group G. Clealy the ring of all integers of K is an [G]-module, and the purpose of this paper is to give a necessary and sufficient condition for the [G]-module to be indecomposable.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 73 , March 1979 , pp. 61 - 68
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Miyata, Y., On the module structure of the ring of all integers of a p-adic, number field, Nagoya Math. J. 54 (1974), 53–59.Google Scholar
[2] Serre, J. P., Corps Locaux, Paris, 1962.Google Scholar
[3] Wyman, B. F., Wildly ramified gamma extension, Amer. J. Math. 91 (1969), 135–152.CrossRefGoogle Scholar