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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On stable noetherian rings


Author: Zoltán Papp
Journal: Trans. Amer. Math. Soc. 213 (1975), 107-114
MSC: Primary 16A46
MathSciNet review: 0393120
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Abstract: A ring R is called stable if every localizing subcategory of $ _R{\text{M}}$ is closed under taking injective envelopes. In this paper the stable noetherian rings are characterized in terms of the idempotent kernel functors of $ _R{\text{M}}$ (O. Goldman [5]). The stable noetherian rings, the classical rings (Riley [11]) and the noetherian rings ``with sufficiently many two-sided ideals'' (Gabriel [4]) are compared and their relationships are studied. The close similarity between the commutative noetherian rings and the stable noetherian rings is also pointed out in the results.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0393120-1
PII: S 0002-9947(1975)0393120-1
Keywords: Stable localizing subcategory, kernel functor, prime kernel functor, stable ring, SMI-ring, classical ring
Article copyright: © Copyright 1975 American Mathematical Society