[Haskell-cafe] Re: Num instances for 2-dimensional types

[Daniel Fischer]

Am Mittwoch 07 Oktober 2009 22:44:19 schrieb Joe Fredette:
> A ring is an abelian group in addition, with the added operation (*)
> being distributive over addition, and 0 annihilating under
> multiplication. (*) is also associative. Rings don't necessarily need
> _multiplicative_ id, only _additive_ id. Sometimes Rings w/o ID is
> called a Rng (a bit of a pun).
>
> /Joe

In my experience, the definition of a ring more commonly includes the multiplicative 
identity and abelian groups with an associative multiplication which distributes over 
addition are called semi-rings.

There is no universally employed definition (like for natural numbers, is 0 included or 
not; fields, is the commutativity of multiplication part of the definition or not; 
compactness, does it include Hausdorff or not; ...).