Abstract
It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.
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Yakovlev, A.V. On p-Extensions of Fields of Characteristic p . Journal of Mathematical Sciences 120, 1642–1644 (2004). https://doi.org/10.1023/B:JOTH.0000017894.66521.34
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DOI: https://doi.org/10.1023/B:JOTH.0000017894.66521.34