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

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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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     author = {Simis, Aron},
     title = {On {א\ensuremath{\alpha}-Noetherian} {Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {245--247},
     year = {1970},
     volume = {13},
     number = {2},
     doi = {10.4153/CMB-1970-049-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-049-2/}
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