The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure
نویسندگان
چکیده
For an odd prime number p, we consider degree p extensions L/K of p-adic fields with normal closure L˜ such that the Galois group L˜/K is dihedral order 2p. We shall prove a complete characterization freeness ring integers OL over its associated AL/K in unique Hopf-Galois structure on L/K, which analogous to one already known for cyclic fields. derive positive and negative results criteria as AL/K-module.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2023
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.10.002