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Left artinian algebraic algebras

Akbari, S ; Sharif University of Technology | 2001

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  1. Type of Document: Article
  2. Publisher: 2001
  3. Abstract:
  4. Let R be a left artinian central F-algebra, T(R) = J(R) + [R,R], and U(R) the group of units of R. As one of our results, we show that, if R is algebraic and char F = 0, then the number of simple components of R = R/J(R) is greater than or equal to dimF R/T(R). We show that, when char F = 0 or F is uncountable, R is algebraic over F if and only if [R, R] is algebraic over F. As another approach, we prove that R is algebraic over F if and only if the derived subgroup of U(R) is algebraic over F. Also, we present an elementary proof for a special case of an old question due to Jacobson. © Inst. Math. CAS 2001
  5. Keywords:
  6. Algebraic algebras ; Artinian rings ; Division rings ; Semisimple rings
  7. Source: Algebra Colloquium ; Volume 8, Issue 4 , 2001 , Pages 463-470 ; 10053867 (ISSN)