Galois Module Structure of the Integers in Wildly Ramified Cyclic Extensions

AbstractThis work is concerned with the Galois module structure of the ring of integers in totally ramified cyclic extensions, L/K, of local fields whose characteristic is zero, [L:K] = pm, m arbitrary and p an odd prime. Under a restriction on the first ramification number, the structure of the ring of integers of L is described in terms of explicit indecomposable Zp[G]- modules, G denoting the Galois group and Zp, the ring of p-adic integers. This explicit description is an extension of the results in a recent paper of M. Rzedowski-Calderón, G. D. Villa-Salvador, and M. L. Madan (1990, Math. Z. 204, 401-424)