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3 results

  • On the Associated Lie Ring and the Adjoint Group of a Radical Ring

  • Hartmut Laue
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 2 / 01 June 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 215-222
    Print publication:
    01 June 1984
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  • We investigate connections between the associated Lie ring and the adjoint group of a radical ring, studying their upper central chains. Part of a conjecture of S. A. Jennings is proved, and one of our results improves a theorem of his.

  • Solvable Groups of Unipotent Elements in a Ring

  • Abraham A. Klein
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 2 / 01 June 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 187-190
    Print publication:
    01 June 1982
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  • Let R be a ring with 1 whose nil subrings are nilpotent modulo the sum of nilpotent ideals. It is proved that if G is a locally solvable group of unipotent elements in R, then the subring generated by {g −1 g ∈ G} is nil. This result implies a result of Sizer showing that a solvable group of unipotent matrices over a skew field can be simultaneously triangularized.