Exercise
With which ring is the residue class ring Z/4Z[X]/({2, X2}) isomorphic?
Z/4Z
Z/2Z × Z/2Z
Neither of the above
No,
2 * 1 = 0 in our ring, but not in Z/4Z.
No. Amongst
the residue classes of 0, 1, X, X + 1, no two
distinct ones occur whose product is 0, but in
Z/2Z × Z/2Z, there are.
Yes.