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Simple rings without zero-divisors, and Lie division rings

Published online by Cambridge University Press:  26 February 2010

P. M. Cohn
The University, Manchester 13.
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Let R be a simple ring. If R contains at least one minimal nonzero one-sided ideal, then R has zero-divisors, unless R is a division ring. However, simple rings exist which are not division rings and have no zero-divisors. Our present object is to prove the following embedding theorem:

Theorem 1. Every ring R without zero-divisors may be embedded in a simple ring R* without zero-divisors. If there is a non-zero element ƒ in R satisfying ƒ2 = nƒ, where n is an integer, then R* necessarily has a unit-element; otherwise R* may be chosen to have no unit-element.

Research Article
Copyright © University College London 1959

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