On the Invariant Factors of Kummer Orders in the Rings of Integers of p-adic Number Fields of Degreep2

Miyata, Yoshimasa

doi:10.1006/jnth.1997.2170

Journal of Number Theory

1997

DOI: 10.1006/jnth.1997.2170

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On the Invariant Factors of Kummer Orders in the Rings of Integers of p-adic Number Fields of Degreep2

Yoshimasa Miyata

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2007

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On Galois structure of the integers in elementary abelian extensions of local number fields

Miyata

2007

Journal of Number Theory

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Let p be an odd prime number and k a finite extension of Q p . Let K/k be a totally ramified elementary abelian Kummer extension of degree p 2 with Galois group G. We determine the isomorphism class of the ring of integers in K as an oG-module under some assumptions. The obtained results imply there exist extensions whose rings are Z p G-isomorphic but not oG-isomorphic, where Z p is the ring of p-adic integers. Moreover we obtain conditions that the rings of integers are free over the associated orders and give extensions whose rings are not free.

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On Galois structure of the integers in elementary abelian extensions of local number fields

Miyata

2007

Journal of Number Theory

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On the Invariant Factors of Kummer Orders in the Rings of Integers of p-adic Number Fields of Degreep2

Cited by 1 publication

References 6 publications

On Galois structure of the integers in elementary abelian extensions of local number fields

On Galois structure of the integers in elementary abelian extensions of local number fields

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