Galois Module Structure of the Integers in Wildly Ramified Cyclic Extensions Original Research Article

This 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).