Let R = ℤ[X]/(x2 + 1) and ψ : ℤ[X] → R be the natural quotient map. Which of the following statements are true?
1
R is isomorphic to a subring of ℂ.
2
For any prime number p ∈ℤ , the ideal generated by ψ(p) is a proper ideal of R.
3
R has infinitely many prime ideals.
4
The ideal generated by ψ(X) is a prime ideal in R.