Distributive multiplication rings

S. Feigelstock, R. Raphael

Research output: Contribution to journalArticlepeer-review


A ring R 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,...,an ∋R. It will be shown that the semi-primitive left (right)n-distributive rings are precisely the generalized boolean rings A 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 ring N satisfying Nn+1=0 by a generalized boolean ring described above. Under certain circumstances it will be shown that this extension splits.

Original languageEnglish
Pages (from-to)161-165
Number of pages5
JournalPeriodica Mathematica Hungarica
Issue number2
StatePublished - Oct 1992


  • Mathematics subject classification numbers, 1991: Primary 16A48
  • boolean ring
  • n-distributive multiplication ring


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