Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Algebra Rings & Ideals
Let R be a ring and N the set of nilpotent elements, i.e.
N = {x ∈ R|xn = 0 for some n ∈ ℕ}.
Which of the following is true?
1
N is an ideal in R.
2
N is never an ideal in R.
3
If R is non‐commutative, N is not an ideal.
4
If R is commutative, N is an ideal.
5
Question Not Attempted