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Periodica Mathematica Hungarica

, Volume 25, Issue 2, pp 161–165 | Cite as

Distributive multiplication rings

  • S. Feigelstock
  • R. Raphael
Article

Abstract

A ringR is said to be a left (right)n-distributive multiplication ring, n>1 a positive integer, if aa1a2...an=aa1aa2...aan (a1a2...ana=a1aa2a...ana) for all a, a1,...,anR. It will be shown that the semi-primitive left (right)n-distributive rings are precisely the generalized boolean ringsA satisfying an=a for all a ∋A. An arbitrary left (right)n-distributive multiplication ring will be seen to be an extension of a nilpotent ringN satisfyingNn+1=0 by a generalized boolean ring described above. Under certain circumstances it will be shown that this extension splits.

Mathematics subject classification numbers, 1991

Primary 16A48 

Key words and phrases

n-distributive multiplication ring boolean ring 

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References

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    R. P.Sullivan, Research problems,Period. Math. Hung. 8 (1977), 313–314.Google Scholar

Copyright information

© Akadémiai Kiadó 1992

Authors and Affiliations

  • S. Feigelstock
    • 1
  • R. Raphael
    • 2
  1. 1.Bar Ilan UniversityRamat-GanIsrael
  2. 2.Concordia UniversityMontrealCanada

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