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2 results

  • Finiteness Conditions for Near-Rings

  • H. E. Heatherly, J. D. P. Meldrum
  • Journal:
    Canadian Mathematical Bulletin / Volume 35 / Issue 4 / 01 December 1992
    Published online by Cambridge University Press:
    20 November 2018, pp. 492-496
    Print publication:
    01 December 1992
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  • There have been a number of papers which give necessary conditions for a ring to be finite, and a few, most notably H. E. Bell [1], which do the same for near-rings. We wish to make a contribution to this latter theme. Most of Bell's results concern distributive near-rings. Our main contribution is to extend a number of these results to weakly distributive near-rings.

  • A Note on Partition-Inducing Automorphism Groups

  • Martin R. Pettet
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 2 / 01 June 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 157-159
    Print publication:
    01 June 1984
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  • We consider a finite group G with a group A acting on it in such a way as to induce a partition of G# (a situation which arises in the study of centralizer near-rings). With the additional hypothesis that (|Aω|, |G|) = 1, it is shown that either A is semiregular on G# or G is an irreducible module for A.