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