Ideals of an abelian p-extension of a local field as Galois modules

Ideals of the ring of integers of an Abelian p-extension of a local field (a finite extension of the field of p-adic numbers) are studied as modules with operators from the Galois group of the extension. Necessary and sufficient conditions are found for the decomposability of these ideals as Galois modules. When the decomposability conditions are satisfied, the decomposition of the ideal into indecomposable summands is found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 57, pp. 64–84, 1976.