Geodesic
On אα-Noetherian Modules
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 245-247

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we define two concepts which can be thought of as a generalization of noetherian concepts.The main result is as follows (Corollary A): If R is a ring whose countably generated (left) ideals are (left) principal, then R is a (left) principal ideal ring.This result if obtained, more generally, for any (left) R-module and any regular cardinal אα (Corollary 1); a cardinal אα is regular whenever W(אα) = {ordinals γ | card γ < אα} has no cofinal subset of cardinality less than אα. 
Simis, Aron. On אα-Noetherian Modules. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 245-247. doi: 10.4153/CMB-1970-049-2
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[3] 3. Ribenboim, P., La conjecture d' Artin sur les equations diophantiennes, Queen's University, 1968. Google Scholar

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