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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeJul 13th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItex[[near-ring]]

   near-ring

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 3rd 2013
   • (edited Nov 3rd 2013)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWikipedia [page](http://en.wikipedia.org/wiki/Near-ring) 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]].

   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.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeNov 5th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItex> Wikipedia page does not require that the multiplicative semigroup of a near-ring has a unit Obviously, that would be a near-rng. (-:

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

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

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeNov 5th 2013
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWell, 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).

   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).

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeNov 5th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThe 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.

   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.

6. • CommentRowNumber6.
   • CommentAuthorzskoda
   • CommentTimeNov 5th 2013
   • (edited Nov 5th 2013)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexSo, 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]].

   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.