Exercise
Put d = 2X+1. In which of the following cases is the map j of the lemma not injective?
R = Z/6Z
R = Z/7Z
R = Z/9Z
Indeed, j(3) = 3 + (d) = 3 + 6X + (d) = (d)= j(0).
No, j is injective since 7 is a prime number.
Despite the fact that 9 is not a prime number, j is still injective.
(Can you prove this?)