Hi there,
> > Is there any real reason to use "Modules(R)" as "Bimodules(R,R)"
> > beyond the comfort of not changing the names? If not, I'd strongly
> > suggest forgetting the name "Modules" for noncommutative rings or
> > default it to left modules.
>
> Oh, interesting that you say that. That is exactly what PanAxiom is doing:
>
> Module(R:CommutativeRing): Category == BiModule(R,R)
> add
> if not(R is %) then x:%*r:R == r*x
>
> Module(R) can only be instatiated if R is a commutative ring.
> To make it more clear:
>
> (1) -> S2:=SquareMatrix(2, Integer)
>
> (1) SquareMatrix(2,Integer)
> Type: Domain
> (2) -> SparseUnivariatePolynomial(S2) has Module(S2)
>
> Module(S2) is not a valid type.
>
> Isn't that what you want? Maybe you should use FriCAS. ;-)
So that you certainly have two other categories RightModule and LeftModule.
Here I see two possibilities:
1 - Restrict Module to the commutative case and create RightModule and
LeftModule and define
Module(R) := Bimodule(R,R)
Module(L,R) := Join(LeftModule(L), RightModule(R))
2 - Define Module as an alias for LeftModule.
Module(L,R) := Join(LeftModule(L), RightModule(R))
In my experience, in the commutative case, we never use the two sided case. EG
if v is in a R-vector space, I always write 3*v and never v*3...
What's your preferred choice ?
Cheers,
Florent
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