Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T10:34:05.099Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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