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 deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeJun 9th 2015
    • (edited Jun 9th 2015)

    Someone anonymous has changed the wording in coherent module. I think it is correct but it is a bit incoherent. They changed ’Noetherian ring’ to ’coherent ring’ but have not defined that concept. Can someone who knows the terminology better than me check this out? It probably just needs a line saying what a coherent ring is.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJun 9th 2015

    One of the papers in the Borel’s volume on D-modules has theory of coherent rings/algebras in elementary detail. I will check later…

    • CommentRowNumber3.
    • CommentAuthorDexter Chua
    • CommentTimeSep 9th 2016

    The definition of a coherent module seems to differ from other sources such as Stacks Project. The other definitions only require finitely-generated submodules to be finitely presented, and not all of them. Can someone more familiar with modules confirm?

    (Also, the usual definition says the module has to be finitely generated and finitely-generated submodules are finitely presented. That implies that the module itself is also finitely-generated, right?)

  1. Yes, thanks for your note, I just fixed the entry. One should only require the finitely-generated submodules to be finitely presented. Else the condition would be the same as Noetherianity. Also the condition wouldn’t make any sense in constructive mathematics, where one can’t even show that all submodules of \mathbb{Z} are finitely generated.

    Indeed the module itself is finitely generated.

    • CommentRowNumber5.
    • CommentAuthorJohn Baez
    • CommentTimeOct 1st 2021

    Removed unnecessary and distracting definition of noetherian ring; fixed spelling here and there, etc.

    diff, v8, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2021

    I have cleaned up and cross-linked a little more.