[Haskell-cafe] What's this algebraic structure called?

[Derek Elkins]

On Tue, 2008-10-28 at 15:43 +1300, Richard O'Keefe wrote:
> On 28 Oct 2008, at 2:54 pm, Derek Elkins wrote:
> 
> > On Tue, 2008-10-28 at 13:54 +1300, Richard O'Keefe wrote:
> >> Is there a special name for an operator monoid where the
> >> structure that's acted on is an Abelian group?
> >
> > This should just be equivalent to a ring, maybe without  
> > distributivity.
> > Maybe missing some other properties depending on what you mean by
> > "operator."
> 
> Yes, it's close to a ring, but we have ((M,*,1),(X,+,0,-))
> where (M,*,1) is the monoid and (X,+,0,-) is the Abelian group.
> For what I have in mind the sets M and X are disjoint.
> For a ring they would be identical.
> (This being Haskell-Café, I knew types would come in useful...)

Some variation on a module then:
http://en.wikipedia.org/wiki/Module_(mathematics)