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The group of units of an Artinian ring

Akbari, S ; Sharif University of Technology | 2002

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  1. Type of Document: Article
  2. Publisher: 2002
  3. Abstract:
  4. 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 GL n (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. © Inst. Math. CAS 2002
  5. Keywords:
  6. Artinian rings ; Division rings ; Finitely generated ; Maximal subgroups
  7. Source: Algebra Colloquium ; Volume 9, Issue 1 , 2002 , Pages 81-88 ; 10053867 (ISSN)