Hi,

Let Z[X,Y] be the ring of polynomials in variables x and Y with integer coefficients.I is the following ideal:

I=(x+y)Z[x,y]+3*Z[x,y].

Prove that the quotient ring Z[x,y]/I is isomorphic to the ring of polynomials in x and coefficients in Z/3Z

I tried using the homomorphism theorem for rings,and I need help with the propriate homomorphism from Z[x,y] onto the ring (Z/3Z)[X]

Thanks in advance.