Exercise
Consider the ring R = Z/4Z×Z/8Z and its subset V = {(2,2),(2,6)}. Which is the ideal of R generated by V?
{(0,0), (2,0), (2,2), (2,4), (2,6), (0,2), (0,4), (0,6)}
{(0,0), (2,2), (2,6), (0,4)}
R
Right!
No. Multiply the first element by (1,0).
Wrong. V consists of zero divisors
only, and hence so does the ideal generated by V.