If x in T and y in T then xy in T (why?)
Thus, phi(x+y)=phi(x)+phi(y) thus, phi(x)+phi(x) in Y[T].
And phi(0) is identity element.
And phi(x^-1) is inverse.
And it is associative because R is associative.
So it is commutative.
This show that <Y[T],+> forms abelian group.
I leave it to you to show everything else.
The same idea appiles.