CM2015:P000010

On the structure of the special linear group over rings with dimension one

*Jinwang Liu (Hunan University of Science and Technology)

We prove that for any uniserial ring ${\bf R}$ of Krull dimension $\le 1$ and $n\ge 3$,
the group $SL_n({\bf R}[x])=E_n({\bf R}[x])$, and for any arithmetical ring ${\bf R}$ of Krull dimension $\le 1$ and $n\ge 3$, the group $SL_n({\bf R}[x])=SL_n({\bf R})\cdot E_n({\bf R}[x])$. These solve partly two Yengui's conjectures.

We prove that for any uniserial ring ${\bf R}$ of Krull dimension $\le 1$ and $n\ge 3$, the group $SL_n({\bf R}[x])=E_n({\bf R}[x])$, and for any arithmetical ring ${\bf R}$ of Krull dimension $\le 1$ and $n\ge 3$, the group $SL_n({\bf R}[x])=SL_n({\bf R})\cdot E_n({\bf R}[x])$. These solve partly two Yengui's conjectures.

第七届全国计算机数学学术会议

On the structure of the special linear group over rings with dimension one