Let K/k be a cyclic totally ramified Kummer extension of degree p(n) with Galois group G. Let D and o be the rings of integers in K and k. respectively. For n = 1, F. Bertrandias and M.-J. Ferton determined the ring End(oG)(D) of oG-endomorphisms of D and L.N. Childs constructed the maximal order S in D whose ring of oG-endomorphisms is a Hopf order. A Hopf order whose linear dual is a Larson order in kG is called a dual Larson order. In this paper, the generators of a dual Larson order are given. We determine EndoG(D) and obtain a maximal dual Larson order contained in End(oG)(D). We construct a Hopf Galois extension S in D, whose ring H(S) of oG-endomorphisms is a dual Larson order. We affirm an order S' in D with a dual Larson order H(S) is a tame H(S')-extension and show that S is maximal in such orders S. (C) 2004 Elsevier Inc. All rights reserved.
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