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A note on intermediate normalising extensions
Published online by Cambridge University Press: 17 April 2009
Abstract
We prove that the following ring-theoretic properties are shared by the two rings involved in a normalising extension R ⊂ S, and that these properties are inherited by any intermediate extension: semilocal, left perfect, semiprimary. This transfer fails for the nilpotency of the Jacobson radical. However, if the normalising set is a basis for the left R-module S, then the nilpotency of the Jacobson radical behaves in the same way as the three properties mentioned above.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 313 - 316
- Copyright
- Copyright © Australian Mathematical Society 1994