Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: Artinian local ring

Bottom of Page

1 to 4 of 4

  1.  

  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

1 to 4 of 4

  1.