Originally Posted by

**knguyen2005** Thanks Tonio for a quick reply

In part (a), we just need to use definition to show that F(R) isa commutative ring

i.e.

(i) (F(R),+) is an Abelian group

(ii) (F(R),.) is monoid

(iii) . is ditributive over +

And plus, for all f, g in F(R), f.g = g.f (Commutative)

Then we conclude that F(R) is a commutative ring. Is that enough ? Or we have to show that F(R) is not an integral domain? Or it automatically follow from the proof that F(R) is a commutative ring then F(R) is not an integral domain?

In part (b), To show that D(R)=<C(R)=<F(R). I can use the results from analysis (sandwich rule) to prove it but I forgot how to do it?

Also, we have to calculate F(R)* and U(F(R)). It is different, F(R)* is a ring with non-zero elements in it. And U(F(R)) is unit of the ring

I hope it does make sense to you