论文标题
定义R和G（R）
Defining R and G(R)
论文作者
论文摘要
我们表明，对于奇瓦利组G（r），在一个环上至少2个级别的g（r），根部亚组本质上是（几乎总是）相应根部元素的双中心化。在许多情况下，这意味着R和G（R）是双重解剖的，在各种环和田地上为代数组提供了一种新方法。对于这样的组，它遵循的是，在相应的环类中，r可以有限的r可以有限的公理化组中的G（r）有限的公理化。
We show that for Chevalley groups G(R) of rank at least 2 over a ring R the root subgroups are essentially (nearly always) the double centralizers of corresponding root elements. In very many cases this implies that R and G(R) are bi-interpretable, yielding a new approach to bi-interpretability for algebraic groups over a wide range of rings and fields. For such groups it then follows that the group G(R) is finitely axiomatizable in the appropriate class of groups provided R is finitely axiomatizable in the corresponding class of rings.
