Abstract
Necessary and sufficient conditions are found under which the Abelian ideal of the p-extension of an irregular local field, treated as a module with operators from the Galois group, is decomposable. In the decomposable case, the decomposition of the ideal into indecomposable terms is found.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 14–35, 1974.
The author thanks Z. I. Borevich for guidance, and A. V. Yakovlev for valuable comments.
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Vostokov, S.V. Ideals of an Abelian p -extension of an irregular local field as Galois modules. J Math Sci 9, 299–317 (1978). https://doi.org/10.1007/BF01085048
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DOI: https://doi.org/10.1007/BF01085048