Galois extensions and $$O^{*}$$-fields
Galois extensions and $$O^{*}$$-fields
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伽罗瓦扩展和 $$O^{*}$$-字段
DOI：
10.1007/s11117-023-00982-w
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发表时间：
2023
期刊：
影响因子：
1
通讯作者：
Ma, Jingjing
中科院分区：
文献类型：
--
作者：
Evans, Kenneth;Ma, Jingjing
A fieldFisif构成偏序域的每一个偏序都可以被扩展为使构成Fas是全序域的一个全序。我们使用Dubois和Harison发展的无穷素数理论来证明以下结论。对于有限维环上的子域Fof，我们证明了当Fis Galois环上时，F是-域当且仅当是的子域。我们找到了构成Fan-field的其他条件，并给出了几个例子。对于特征为0的任意域，我们刻画了极大偏序是阿基米德的。
A fieldFisif each partial order that makesFa partially ordered field can be extended to a total order that makesFa totally ordered field. We use the theory of infinite primes developed by Dubois and Harrison to prove the following. For a subfieldFofthat is finite-dimensional over, we prove that whenFis Galois over,Fis an-field if and only if is a subfield of. We find other conditions that makeFan-field and provide several examples. As well for an arbitrary field of characteristic 0, we characterize the maximal partial orders that are Archimedean.