Idempotents in the Endomorphism Ring of an Ideal in a p-Extension of a Complete, Discrete Valuation Field with Residue Field of Characteristic p as a Galois Module

In this paper, the question concerning the existence of nontrivial idempotents in the endomorphism ring of an ideal in a p-extension of a complete discrete valuation field with residue field of characteristic p > 2 as a Galois module is considered. The nonexistence of nontrivial central idempotents for a non-Abelian totally widely ramified extension is proved. Bibliography: 4 titles.