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Faithful Noetherian modules

1973
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Proceedings of the American Mathematical Society
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The Eakin-Nagata theorem says that if T is a commutative Noetherian ring which is finitely generated as a module over a subring R, then R is also Noetherian. This paper proves a generalization of this result. However, the main interest is that the proof is very elementary and uses little more than the definition of "Noetherian". All rings are associative and have a unit, subrings have the same unit, and modules are unitary. A theorem due independently to Eakin [2] and Nagata [7] says that if

doi:10.1090/s0002-9939-1973-0379477-x
fatcat:ncq2gn5iejgwfjskq2wwv6z7y4