论文标题
$ p $ - adic领域的扩展与具有正常积分基础有多远？
How far is an extension of $p$-adic fields from having a normal integral basis?
论文作者
论文摘要
令$ l/k $为$ p $ adic领域的有限galois扩展名，带有$ g $。众所周知，$ \ MATHCAL {O} _l $包含一个免费的$ \ MATHCAL {O} _K [g] $ - 有限索引的子模块。我们研究了这种免费的子模块的最小索引，并在几种情况下准确确定它，包括$ p $ $ p $ - 亚种的任何循环扩展。
Let $L/K$ be a finite Galois extension of $p$-adic fields with group $G$. It is well-known that $\mathcal{O}_L$ contains a free $\mathcal{O}_K[G]$-submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree $p$ of $p$-adic fields.
