Geodesic
Minimally Generated Modules
Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 103-105

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DOI

A non-zero module M having a minimal generator set contains a maximal submodule. If M is Artinian and all submodules of M have minimal generator sets then M is Noetherian; it follows that every left Artinian module of a left perfect ring is Noetherian. Every right Noetherian module of a left perfect ring is Artinian. It follows that a module over a left and right perfect ring (in particular, commutative) is Artinian if and only if it is Noetherian. We prove that a local ring is left perfect if and only if each left module has a minimal generator set.
DOI : 10.4153/CMB-1980-014-1
Mots-clés : 1610, 1640, 1650, Minimal generator set, perfect ring, Noetherian module, Artinian module, socle, injective module, finitely generated 
Rant, W. H. Minimally Generated Modules. Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 103-105. doi: 10.4153/CMB-1980-014-1
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     title = {Minimally {Generated} {Modules}},
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     year = {1980},
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     doi = {10.4153/CMB-1980-014-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-014-1/}
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