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: rig

Bottom of Page

1 to 17 of 17

  1.  
    • CommentRowNumber1.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 2nd 2022

    Added link to “multiplicatively cancellable semi-ring”.

    diff, v32, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeAug 3rd 2022

    Semirings as defined on Wolfram MathWorld don’t have either an additive or multiplicative identity; they are semigroup objects in the category of commutative semigroups.

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeAug 3rd 2022
    • CommentRowNumber4.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 3rd 2022
    • (edited Aug 3rd 2022)

    Thank you, it seems very logical to me now. I will use the term rig for the structure with the two identities from now on.

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeAug 3rd 2022

    I’ve seen four different definitions of a “semiring” out there, depending on the author:

    • A semigroup object in the category of commutative semigroups
    • A monoid object in the category of commutative semigroups
    • A semigroup object in the category of commutative monoids
    • A monoid object in the category of commutative monoids

    The problem is already there in the definition of a ring, as some authors define a ring to be a semigroup object in the category of abelian groups, while other authors define a ring to be a monoid object in the category of commutative monoids

    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeAug 3rd 2022

    *define a ring to be a monoid object in the category of abelian groups

  7. adding paragraph on the relationship between rigs and semirings.

    Anonymous

    diff, v35, current

    • CommentRowNumber8.
    • CommentAuthorJ-B Vienney
    • CommentTimeAug 18th 2022

    Added a reference to Rig

    diff, v38, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2023

    added pointer to

    • William Lawvere, pp. 1 of: Introduction to Linear Categories and Applications, course lecture notes (1992) [pdf]

    Is this (on p. 2) maybe the actual origin of the term “rig”?

    diff, v40, current

    • CommentRowNumber10.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 25th 2023

    It appears earlier than 1992, e.g., in

    • S.H. Schanuel, Negative sets have Euler characteristic and dimension, in: Proceedings of Category Theory, Como, Italy,1990, in: Lecture Notes in Mathematics, vol. 1488, Springer-Verlag, 1991, pp. 379–385.

    See here, page 379. But I wouldn’t bet this is the earliest appearance either.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 26th 2023

    Thanks, I have added that to the entry.

    diff, v41, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2023

    Thanks to a reference provided by Rod McGuire in another thread (here):

    we can settle the question of origin of the terminology ’rig’ – because Lawvere writes there, about his work with Schanuel, that:

    We were amused when we finally revealed to each other that we had each independently come up with the term ’rig’.

    Have added this to the entry.

    diff, v42, current

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

    Anonymouse

    diff, v47, current

    • CommentRowNumber14.
    • CommentAuthorJohn Baez
    • CommentTimeNov 10th 2024

    For some reason this passage wasn’t showing in the definition of rig:

    and also the absorption/annihilation laws, which are the nullary version of the distributive laws:

    0⋅x=0=x⋅00\cdot x = 0 = x\cdot 0

    I’m trying to fix that.

    diff, v48, current

    • CommentRowNumber15.
    • CommentAuthorJohn Baez
    • CommentTimeNov 10th 2024

    The problem was apparently a comma directly after a double dollar sign! Removing this made the following text appear.

    diff, v48, current

  16. Adding references

    • Manfred Droste, Werner Kuich, Semirings and Formal Power Series (2009). In: Manfred Droste, Werner Kuich, Heiko Vogler (editors), Handbook of Weighted Automata. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. pp. 3–28.(doi:10.1007/978-3-642-01492-5_1)

    • Zoltán Ésik, Iteration semirings (2008). In: Masami Ito, Masafumi Toyama (editors), Developments in language theory. 12th international conference, DLT 2008, Kyoto, Japan, September 16–19, 2008. Proceedings. Lecture Notes in Computer Science. Vol. 5257. Berlin: Springer-Verlag. pp. 1–20. (doi:10.1007/978-3-540-85780-8_1)

    Anonymouse

    diff, v49, current

  17. Adding reference

    Anonymouse

    diff, v49, current

1 to 17 of 17

  1.