On stable noetherian rings

Papp, Zoltán

doi:10.1090/S0002-9947-1975-0393120-1

On stable noetherian rings
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by Zoltán Papp

Trans. Amer. Math. Soc. 213 (1975), 107-114

DOI: https://doi.org/10.1090/S0002-9947-1975-0393120-1

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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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