Question: Any idea how to implement a group ring?

I'm interested in created a group ring, but have no idea how to do it.

In short, a group ring is a free module with the scalars as elements of a ring,R, and the vectors as elements in a group, G. [Wikipedia has a decent description.]

Elements a=r0*g0 and b=r1*g1 have sum a+b=r0*g0+r1*g1 and product a*b=r0*r1*g0*g1

The distributive property is followed.


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