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A note on intermediate normalising extensions

Published online by Cambridge University Press:  17 April 2009

S. Dăscălescu  and
L. van Wyk
S. Dăscălescu
Affiliation:
Facultatea de Matematica University of BucharestStr. Academiai 14 R70109 Bucharest 1Romania
L. van Wyk
Affiliation:
Department of MathematicsUniversity of StellenboschStellenbosch 7600South Africa E-mail: [email protected]
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Abstract

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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

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