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).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 13th 2013
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 3rd 2013
    • (edited Nov 3rd 2013)

    Wikipedia page does not require that the multiplicative semigroup o a near-ring has a unit, hence they require a multiplicative semigroup but not a monoid.

    I created a microstub near-field and an entry quasifield, the latter motivated by synthetic projective geometry.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeNov 5th 2013

    Wikipedia page does not require that the multiplicative semigroup of a near-ring has a unit

    Obviously, that would be a near-rng. (-:

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 5th 2013

    Well, I think that the terminology quasiring, semiring, near-ring is not that logically devised; the terms came in different mathematical subdisciplines and have their own conventions. Do you really suggest that the literature is not compatible with wikipedia this time ? (I did not have enough time to look at it; besides considering nonunital rings as rings is not rare in noncommutative ring theory).

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeNov 5th 2013

    The category theorists’ work from whom I learned the concept definitely use the word to have a unit. If the literature is inconsistent, then we should feel free to make a more consistent choice ourselves, e.g. semi- means without units, near- means without distributivity, etc.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeNov 5th 2013
    • (edited Nov 5th 2013)

    So, we need to list concrete references for both and list the areas of each usage to best of our knowledge. And have a note at historical notes on quasigroups.