部分有序场和积分域

Order Pub Date : 2024-07-09 DOI:10.1007/s11083-024-09667-9

Jingjing Ma

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引用次数: 0

摘要

文章研究了有理数代数域上的划分封闭偏序。特别地，文章使用从给定域到复数域的嵌入来描述最大偏序。第 2 节研究了在\(\mathbb {Q}\)上不是有限维的\(O^{*}\)场，第 3 节考虑了在完全有序场上的\(n^{th}\)根函数。

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Partially Ordered Fields and Integral Domains

The article studies the division closed partial orders on fields that are algebraic over the field of rational numbers. In particular, the maximal partial orders are described using embeddings from the given field to the field of complex numbers. The \(O^{*}\)-fields that are not finite dimensional over \(\mathbb {Q}\) are studied in Section 2 and the \(n^{th}\)-root function over totally ordered fields is considered in Section 3.

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