Consider the ring \(\rm R=\left\{\Sigma_{n \in Z} a_n X^n \left|a_n \in Z; \ and \ a_n \ne 0\ only\ for\ finitely\ many \ n \in Z\right.\right\}\) where addition and multiplication are given by \(\rm \Sigma_{n \in Z}a_n X^n+\rm \Sigma_{n \in Z}b_n X^n=\rm \Sigma_{n \in Z}(a_n+b_n)X^n\)
\(\rm \left(\rm \Sigma_{n \in Z}a_n X^n\right)\rm (\Sigma_{n \in Z}b_m X^m)=\rm \Sigma_{k \in Z}(\Sigma_{n+m=k}a_nb_m) X^k\)
Which of the following statements is true?
1
R is not commutative
2
The ideal (X - 1) is a maximal ideal in R
3
The ideal (X - 1, 2) is a prime ideal in R
4
The ideal (X, 5) is a maximal ideal in R