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Essential extensions in radical theory for rings

Published online by Cambridge University Press:  09 April 2009

G. A. P. Heyman  and
C. Roos
C. Roos
Affiliation:
Department of Mathematics, University of Technology, Delft, Netherlands.
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Abstract

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The essential cover Mk of a class M is defined as the class of all essential extensions of rings belonging to M. M is called essentially closed if Mk = M. Every class M has a unique essential closure, i.e. a smallest essentially closed class containing M.

Let M be a hereditary class of (semi)prime rings. Then M is proved to be a (weakly) special class if and only if M is essentially closed. A main result is that Mk is the smallest (weakly) special class containing M. Further it is shown that the upper radical UM determined by M, is hereditary if and only if UM has the intersection property with respect to Mk.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 340 - 347
Copyright
Copyright © Australian Mathematical Society 1977

References

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