Distributive multiplication rings

S. Feigelstock; R. Raphael

doi:10.1007/bf02113172

Distributive multiplication rings

S. Feigelstock, R. Raphael

Department of Mathematics

Concordia University

Research output: Contribution to journal › Article › peer-review

Abstract

A ring R is said to be a left (right)n-distributive multiplication ring, n>1 a positive integer, if aa₁a₂...a_n=aa₁aa₂...aa_n (a₁a₂...a_na=a₁aa₂a...a_na) for all a, a₁,...,a_n ∋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 language	English
Pages (from-to)	161-165
Number of pages	5
Journal	Periodica Mathematica Hungarica
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/bf02113172
State	Published - Oct 1992

Keywords

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

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10.1007/bf02113172

Cite this

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AB - 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.

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Distributive multiplication rings

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Keywords

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