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How far is an extension of p-adic fields from having a normal integral basis?
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-07-29 , DOI: 10.1016/j.jnt.2021.06.008 Ilaria Del Corso 1 , Fabio Ferri 2 , Davide Lombardo 1
中文翻译:
p-adic 域的扩展距离具有正规积分基有多远?
更新日期:2021-07-29
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-07-29 , DOI: 10.1016/j.jnt.2021.06.008 Ilaria Del Corso 1 , Fabio Ferri 2 , Davide Lombardo 1
Affiliation
Let be a finite Galois extension of p-adic fields with group G. It is well-known that contains a free -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.
中文翻译:
p-adic 域的扩展距离具有正规积分基有多远?
让 是具有群G的p进场的有限伽罗瓦扩展。众所周知, 包含一个免费的 - 有限索引的子模块。我们研究了最小的这样一个自由子模块的指标,准确地确定它在一些情况下,包括度的任何循环扩展p的p进制领域。