论文标题
Hopf-Galois度p扩展的P-ADIC领域的整数环，具有正常闭合
The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure
论文作者
论文摘要
对于一个奇数$ $ p $，我们考虑$ p $扩展$ l/k $ p $ p $ - ad的字段，具有正常闭合$ \ widetilde {l} $，使得$ \ widetilde {l}/k $的galois组是dihedral of dihedral of dihedral of dihedral of dord off $ 2p $。 We shall prove a complete characterization of the freeness of the ring of integers $\mathcal{O}_L$ over its associated order $\mathfrak{A}_{L/K}$ in the unique Hopf-Galois structure on $L/K$, which is analogous to the one already known for cyclic degree $p$ extensions of $p$-adic fields.我们将根据$ \ Mathcal {o} _l $作为$ \ Mathfrak {a} _ {l/k} $ - 模块的标准获得正面和负面结果。
For an odd prime number $p$, we consider degree $p$ extensions $L/K$ of $p$-adic fields with normal closure $\widetilde{L}$ such that the Galois group of $\widetilde{L}/K$ is the dihedral group of order $2p$. We shall prove a complete characterization of the freeness of the ring of integers $\mathcal{O}_L$ over its associated order $\mathfrak{A}_{L/K}$ in the unique Hopf-Galois structure on $L/K$, which is analogous to the one already known for cyclic degree $p$ extensions of $p$-adic fields. We shall derive positive and negative results on criteria for the freeness of $\mathcal{O}_L$ as $\mathfrak{A}_{L/K}$-module.
