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Duo Rings: Some Applications to Commutativity Theorems

Published online by Cambridge University Press:  20 November 2018

Howard E. Bell
Howard E. Bell*
Affiliation:
Brock University
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Proofs of commutativity theorems for general rings usually employ the Jacobson structure theory; however, alternative approaches to the "xn = x theorem" [ l, 2] suggest that the power of the Jacobson theory is not required. In this note we prove two commutativity theorems of Herstein in an elementary way. Both proofs involve establishing first that the rings under consideration are duo-rings - rings in which every one-sided ideal is two-sided.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 375 - 380
Copyright
Copyright © Canadian Mathematical Society 1968

References

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