AI 中文总结
该研究针对形式实域，探讨全正域扩张的性质，证明伽罗瓦全正域扩张对应的毕达哥拉斯闭包扩张也全正，还研究相关代数性质并证明贝歇尔猜想的新成立情形。
AI 中文摘要
对于形式实域$F$，我们研究$F$上的全正域扩张$K$。证明若$K/F$是伽罗瓦扩张且全正，则其对应的毕达哥拉斯闭包扩张$K_{\rm py}/F_{\rm py}$也全正。还研究带正交对合的中心单代数在全正域扩张下的弱各向同性与弱双曲性的性质，利用部分结果证明贝歇尔（Becher）猜想的新成立情形。
英文摘要
For a formally real field $F$, we study totally positive field extensions $K$ over $F$. We show that, if $K /F$ is Galois and totally positive then so is the corresponding extension of their pythagorean closures $K_{\rm py}$ over $F_{\rm py}$. We also study the behaviour of weak isotropy and weak hyperbolicity of central simple algebras with an orthogonal involution over totally positive field extensions. We use some of these results to prove new cases for which a conjecture due to Becher holds.
Journal refJournal of Algebra and Its Applications, Vol. 23, No. 02, 2450034 (2024)
