论文标题
差分符号代数的分裂字段
Splitting fields of differential symbol algebras
论文作者
论文摘要
对于$ m \ geq 2 $，我们在特征上不划分$ m $的字段上研究了$ m $ $ m $的符号代数的派生。 $ k $的差分中央简单代数被有限生成的$ k $分割。对于符号代数上的某些派生，我们提供了差异分裂场的明确构造，并在其代数和超越度上提供界限。我们进一步分析了分裂某些差分符号代数的最大子场。
For $m\geq 2$, we study derivations on symbol algebras of degree $m$ over fields with characteristic not dividing $m$. A differential central simple algebra over a field $k$ is split by a finitely generated extension of $k$. For certain derivations on symbol algebras, we provide explicit construction of differential splitting fields and give bounds on their algebraic and transcendence degrees. We further analyze maximal subfields that split certain differential symbol algebras.
