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3 results

  • Généralisation d'un Lemme de Kummer*

  • Klaus Hoechsmann
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 4 / 01 December 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 486-489
    Print publication:
    01 December 1989
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  • If A is a finite abelian group and ZA its integral group ring, consider units u ∊ ZA which have coefficient sum = 1 and are fixed under the involution a —> a-1, a ∊ A. For an odd regular prime p and a p-group A, it is shown that u ≡ 1 mod p if only if u = π(v)v-p, where v is the same kind of unit, and π is the ring endomorphism given by a —> ap, a∊A.

  • Non-Isomorphic Equivalent Azumaya Algebras

  • Lindsay N. Childs
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 3 / 01 September 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 340-343
    Print publication:
    01 September 1987
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  • We explicitly describe an infinite collection of pairs of Azumaya algebras over the ring of integers of real quadratic number fields K which are maximal orders in the usual quaternion algebra over K, hence Brauer equivalent, but are not isomorphic. The result follows from an identification of the groups of norm one units, using the classification of Coxeter.

  • Integral Group Rings Without Proper Units

  • K. Hoechsmann, S.K. Sehgal
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 1 / 01 March 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 36-42
    Print publication:
    01 March 1987
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  • If A is an elementary abelian ρ-group and C one of its cyclic subgroups, the integral group rings ZA contains, of course, the ring ZC. It will be shown below, for A of rank 2 and ρ a regular prime, that every unit of ZA is a product of units of ZC, as C ranges over all cyclic subgroups.