论文标题
遗传性非二氧化碳田地
Hereditarily non-pythagorean fields
论文作者
论文摘要
我们证明，对于$ f_ {pyth} $的每个适当的有限扩展，$ f $的$ f $ clinture $ f_ {pyth} $的每个适当的有限扩展都不是毕达哥拉斯的田野。这类字段包含数字字段和字段$ f $，这些字段和字段$ f $有限地生成超越学位，至少在$ f $的某个子场上。
We prove for a large class of fields $F$ that every proper finite extension of $F_{pyth}$, the pythagorean closure of $F$, is not a pythagorean field. This class of fields contains number fields and fields $F$ that are finitely generated of transcendence degree at least one over some subfield of $F$.
