Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Algebra Rings & Ideals
Let R = \(\mathbb{Z}[x] \) be the ring of polynomials with integer coefficients. Consider the ideal P = (3, x2 + 2) in R then choose the correct option ?
1
P is a prime ideal, because R/P is an integral domain.
2
P is a prime ideal, because 3 and x2 + 2 are irreducible in R.
3
P is not a prime ideal, because R/P is not an integral domain.
4
P is not a prime ideal, because P is not generated by a single element.
5
Question Not Attempted