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On the module structure of a p-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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Throughout this paper, let p be an odd prime. Let k be a -adic number field and be the ring of all integers in k. Let K/k be a finite totally ramified Galois p-extension of degree pn with the Galois group G. Clearly the ring of all integers in K is an [G]-module. In the previous paper [4], we studied [G]-module structure of in a cyclic totally ramified p-extension, and we have obtained the condition for to be an indecomposable [G]-module.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 77 , February 1980 , pp. 13 - 23
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[1] Amano, S., Eisenstein equations of degree p in a -adic field, J. Fac. Sci. Univ. Tokyo 18, No. 1 (1971), 1–21.Google Scholar
[2] Huppert, B., Endlich Gruppen I, Die Grundlehren der math. Wissenshaften, Band 134, Springer-Verlag, Berlin and New York 1967.Google Scholar
[3] Maus, E., Arithmetish disjucte Kõrper, J. reine angew. Math. 226 (1967), 184–203.Google Scholar
[4] Miyata, Y., On the module of a cyclic extension over a -adic number field, Nagoya Math. J. 73 (1979), 61–68.CrossRefGoogle Scholar
[5] Wyman, B. F., Wildly ramified gamma extension, Amer. J. of Math. 91 (1969), 135–152.CrossRefGoogle Scholar