The Group of Units of an Artinian Ring

• 来源期刊: 代数集刊（英文版）
• 关键词: division rings Artinian rings finitely generated maximal subgroups
• 年，卷（期）: 2002,（1）
• 页码范围: 81-88
• 页数: 8页
• 语种: 英文

摘要

Recently, it is shown that, if D is a finite-dimensional division ring,then GLn(D) is not finitely generated. Our object here is to provide a general framework for the groups of units of left Artinian rings. We prove that, if R is an infinite F-algebra of finite dimension over F, then U(R) is not finitely generated.We show that any infinite subnormal subgroup of GLn (D) has no finite maximal subgroup. Also, we prove that for any infinite left Artinian ring R, U(R) has no finite maximal subgroup, which is a result analogous to that for rings.