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nLab > Latest Changes: noetherian ring

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    • CommentRowNumber1.
    • CommentAuthortrefoils
    • CommentTimeApr 9th 2016

    Added to noetherian ring a homological chacaterization: a ring is Noetherian iff arbitrary direct sums of injective modules are injective.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 9th 2016
    • (edited Apr 10th 2016)

    Thanks! Some of that was also mentioned at injective module (corollary 1 and proposition 1).

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeApr 11th 2016

    Here in the proof, the Baer’s criterion is used, which uses AC. Is the result itself depending on AC ?

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 7th 2023

    Added:

    Introduced by Emmy Noether in

    diff, v22, current

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