摘要
P.Chon在[3]中给出了局部环及某些离散赋值环上GL_2(R)的定义关系.J.Silvester在[2]中集中讨论了半局部环上线性群的定义关系.某些讨论K_2的文献也从其他角度揭示了线性群的定义关系(见[3]、[4]).在这篇文章中我们将给出1—fold环与一些常见的附加一定条件的1—fold环(如单位稳定环,单位正则环等)上GL_2(R)的定义关系.
The following identities hold for any associative ring with identity 1:In the present paper, we provedTheorem 1 The relations (l)-(4) and (5') form a complete set of defining relations for GL_2 over 1-fold rings.Theorem 2 The relations (l)-(4) and (5') form a complete set of defining relations for GL_2 over unit stable rings.Theorem 3 The relations (l)-(5) form a complete set of defining relations for GL_2 over 3-fold rings.Theorem 4 The relations (l)-(4) and (5') form a complete set of defining relations for over unit regular rings.
