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

Richard O'Keefe ok at cs.otago.ac.nz
Mon Oct 27 22:43:47 EDT 2008

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...)

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