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On a Theorem of Burgess and Stephenson

Part of: Local rings and generalizations Modules, bimodules and ideals

Published online by Cambridge University Press:  06 December 2018

W. K. Nicholson
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Abstract

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A theorem of Burgess and Stephenson asserts that in an exchange ring with central idempotents, every maximal left ideal is also a right ideal. The proof uses sheaf-theoretic techniques. In this paper, we give a short elementary proof of this important theorem.

Keywords

exchange ringabelian ringleft quasi-duo ring

MSC classification

Primary: 16L60: Quasi-Frobenius rings
Secondary: 16D25: Ideals 16D60: Simple and semisimple modules, primitive rings and ideals
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 603 - 605
Copyright
© Canadian Mathematical Society 2018 

References

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