Let p be an odd prime number. Let k be a
[pfr ]-number field and [ofr ] the ring of all
integers of k with a prime element π. Let K/k
be a cyclic extension with Galois group G, and [Afr ]
the associated order of the ring [Ofr ] of all integers in K:[Afr ]={f∈kG[mid ]f[Ofr ]⊆[Ofr ]}.F. Bertrandias and M-J. Ferton [1] obtained necessary
and sufficient conditions that
[Ofr ] is [Afr ]-free in the case K/k is of degree
p. The purpose of this paper is to study
such conditions in case K/k is a cyclic totally
ramified Kummer extension of degree n=pm.
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