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Weak ideal invariance and orders in Artinian rings

Published online by Cambridge University Press:  17 April 2009

John A. Beachy
John A. Beachy
Affiliation:
Department of Mathematical Sciences, Northern Illinois Unversity, DeKalb, Illinois 60115, USA.
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Abstract

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It Is known that a ring R with Krull dimension is an order in an Artinian ring if R is K-homogeneous and the prime radical N of R is weakly ideal invariant. The notion of weak ideal invariance can be interpreted in torsion theoretic terms, yielding a shorter and more conceptual proof of this result. In addition, it is shown that the orders in Artinian rings which arise in this fashion are precisely those for which R/N is K-homogeneous.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 2 , April 1981 , pp. 255 - 264
Copyright
Copyright © Australian Mathematical Society 1981

References

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