复数域上的有向偏序
Directed partial orders on the complex number field
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中文总结 AI 辅助
本文构造了复数域上的一类有向偏序正锥，利用局部环整闭包和实生成元定义，并证明了等价条件及非格序性质。
中文摘要 AI 辅助
我们构造了一类正锥，使得复数域\C成为一个有向偏序环。这些正锥是利用局部环的整闭包定义的，并与一个超越基和一个选定的实生成元相关联。一个局部化准则也在\Q的每个超越扩张上给出了这样的序。对于固定的系数域，我们证明了两个实生成元定义相同的锥当且仅当它们相差一个仿射映射，该仿射映射具有正的实代数斜率，且平移在该域上是代数的。非零正元素在取逆运算下封闭。这些序中没有一个是格序。
英文摘要
We construct a class of positive cones that make $\C$ into a directed partially ordered ring. The positive cones are defined using integral closures of local rings, associated with a transcendence basis and a chosen real generator. A localization criterion also yields such orders on every transcendental extension of $\Q$. For a fixed coefficient field, we prove that two real generators define the same cone if and only if they differ by an affine map with positive real-algebraic slope and translation algebraic over that field. The nonzero positive elements are closed under inversion. None of these orders is a lattice order.
发表机构
- School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）
- Shanghai Innovation Institute（上海创新研究院）
机构由 AI 辅助整理，请以论文原文为准。
