Exercise
Consider the morphism
2),
f(X) -> f(2).
Which statement about the kernel K of this morphism is true?
K is a maximal ideal.
K is a prime ideal
but not maximal.
K is not prime.
Yes. Each polynomial p
Q[X]\K maps onto an invertible element in
Q + Q2, and so
the ideal generated by {p}
K coincides with Q[X].
Q[X]\K maps onto an invertible element in
Q + Q2, and so
the ideal generated by {p}
K coincides with Q[X].
No; the nonzero elements in Q + Q2 are invertible.
2 are invertible.
No; there are no zero divisors in Q + Q2.
2.