Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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.
Wikipedia page does not require that the multiplicative semigroup of a near-ring has a unit
Obviously, that would be a near-rng. (-:
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).
The category theoristsâ€™ 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.
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.
1 to 6 of 6