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IPM
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YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 502
School of Mathematics
  Title:   The group of units of an Artinian ring
  Author(s): 
1.  H. Momenaee Kermani
2.  S. Akbari
3.  R. Ebrahimian
4.  A. Salehi Golsefidy
  Status:   Published
  Journal: Algebra Colloq.
  No.:  1
  Vol.:  9
  Year:  2002
  Pages:   81-88
  Supported by:  IPM
  Abstract:
Recently, it has been shown that if D is a finite dimensional division ring then GLn(D) is not finitely generated [2]. Our object here is to provide a general framework for the groups of units of the 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 none of infinite subnormal subgroups of GLn(D) has finite maximal subgroup. Also in this article, we prove that for any infinite left artinian ring R, U(R) has no finite maximal subgroup, a result is analogous to one for rings [6].

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