论文标题
当地戒指上的雪佛兰组的常规双纠正性
Regular bi-interpretability of Chevalley groups over local rings
论文作者
论文摘要
在本文中，我们证明，如果$ g（r）=g_π（φ，r）$ $（e（r）=e_π（φ，r））$是（基本的）等级$> 1 $> 1 $，$ r $是本地戒指（$ \ frac {1} {1} {2} $ for loot Systems $ for loot Systems $ for loot Systems $ {\ Mathbf C} _l，{\ Mathbf F} _4，{\ MathBf G} _2 $，并带有$ \ frac {1} {3} $ for $ {\ MATHBF G} _ {2}）$，然后是$ g（r）$（r）$（r）$（或$（r）$（r）$（r）$（r）$（r）是$（r）$（r）是$（r）。由于该定理的结果，我们表明，在本地环（带有列出的限制）上所有雪瓦利组的类是可以定义的，即，如果对于任意的组〜$ h $，我们有$ h \ equivg_π（φ，r），而不是ring $ r'\ equiv equiv r $ $ $ $ h $ h $ r'
In this paper we prove that if $G(R)=G_π(Φ,R)$ $(E(R)=E_π(Φ, R))$ is an (elementary) Chevalley group of rank $> 1$, $R$ is a local ring (with $\frac{1}{2}$ for the root systems ${\mathbf A}_2, {\mathbf B}_l, {\mathbf C}_l, {\mathbf F}_4, {\mathbf G}_2$ and with $\frac{1}{3}$ for ${\mathbf G}_{2})$, then the group $G(R)$ (or $(E(R)$) is regularly bi-interpretable with the ring~$R$. As a consequence of this theorem, we show that the class of all Chevalley groups over local rings (with the listed restrictions) is elementary definable, i.\,e., if for an arbitrary group~$H$ we have $H\equiv G_π(Φ, R)$, than there exists a ring $R'\equiv R$ such that $H\cong G_π(Φ,R')$.
