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nLab > Latest Changes: Artinian local ring

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  1. renaming page to the one used in the Stacks reference, parallel with Artinian ring.

    Anonymous

    diff, v10, current

    • CommentRowNumber2.
    • CommentAuthorjyxu
    • CommentTimeMar 1st 2024
    I don't think the condition that the Jacobson radical is nilradical is sufficient. For a local ring this condition means that there is only one prime ideal, namely the maximal ideal. But there are such commutative rings that are not Noetherian, see e.g. https://math.stackexchange.com/questions/39458/non-noetherian-ring-with-a-single-prime-ideal. Concretely, take a polynomial ring in infinitely many variables over a field and quotient out the square of the maximal ideal (x_1, x_2, ...) generated by the variables. The quotient ring has only one prime ideal but it is not finitely generated.
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2024

    I have adjusted the wording.

    If you have the energy, it would be worth expanding on this point in the entry.

    diff, v14, current

  4. changed higher algebra - contents to algebra - contents in context sidebar

    Anonymouse

    diff, v15, current

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