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On a class of simple rings

Published online by Cambridge University Press:  26 February 2010

P. M. Cohn
P. M. Cohn
Affiliation:
The University, Manchester 13.
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Extract

Our object in this note is to construct rings such that

More generally we prove the following embedding theorem (Theorem 5.1) from which rings satisfying (I) are easily constructed:

Any algebra over a field F which contains no zero-divisors or unit-element may be embedded in an algebra over F satisfying (I).

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 103 - 117
Copyright
Copyright © University College London 1958

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References

1.Jacobson, N., “The equation ”, Bull. American Math. Soc., 50 (1944), 902–905.CrossRefGoogle Scholar
2.Jacobson, N., Structure of Rings (New York, 1956).CrossRefGoogle Scholar
3.Johnson, R. E., “On the equation over an algebraic division ring”, Bull. American Math. Soc., 50 (1944), 202–207.CrossRefGoogle Scholar
4.Kaplansky, I., Infinite Abelian Groups (Ann Arbor, 1954).Google Scholar
5.Kleinfeld, E., “A note on Moufang-Lie rings”, Proc. American Math. Soc, 9 (1958), 72–74.CrossRefGoogle Scholar