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

Ben Franksen ben.franksen at online.de
Fri Oct 9 15:57:56 EDT 2009

Joe Fredette wrote:
> 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.

Yes, this is how I learned it in my Algebra course(*). Though I can imagine
that this is not universally agreed upon; indeed most of the more
interesting results need a multiplicative unit, IIRC, so there's a
justification for authors to include it in the basic definition (so they
don't have to say let-R-be-a-ring-with-multiplicative-unit all the time ;-)


(*) As an aside, this was given by one Gernot Stroth, back then still at the
FU Berlin, of whom I later learned that he took part in the grand effort to
classify the simple finite groups. The course was extremely tight but it
was fun and I never again learned so much in one semester.

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