On the invariant factors of Kummer orders in the rings of integers of p-adic number fields of degree p(2)

[摘要] Let K/k be an extension of degree p(2) over a p-adic number field k with the Galois group G. We study the Galois module structure of the ring D-K of integers in K. We determine conditions under which the invariant factors of Kummer orders <(D-K)over tilde> in D-K of two extensions coincide with each other and give two examples, one of which shows there exist Kummer extensions K and L with D(K) = D(L) such that D-K and D-L are not Z(p)G-isomorphic. The other shows the existence of extensions F and K such that D-F and D-K are isomorphic over Z(p)G but not over D(k)G. (C) 1997 Academic Press.

[发布日期] 1997-10-01