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    • 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.