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 comma 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 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).
  1. division rigs, the rig version of division rings

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorAli Lahijani
    • CommentTimeJul 5th 2021
    Definition 1.3 refers to subtraction, but it's not clear how (if) it can be defined for a rig.
    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 5th 2021

    I guess one could apply the definition in the case that for every pair of elements x,yx,y there is a unique zz such that either x=y+zx=y+z or y=x+zy=x+z. Then it makes sense to define x#yx\# y iff such zz is invertible. This assumption should probably hold if the map to the ring completion is injective, which seems to require that the additive monoid is cancellative.

    One might demand that addition is cancellative in a general division rig, and I guess this might be enough to arrive at the definition otherwise involving subtraction. Or else add this as an explicit hypothesis to this definition, assuming it works.

  2. Corrected typo (missing plural on the word “rational”).

    Anonymous

    diff, v2, current