Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Algebra Rings & Ideals
Let R be a commutative ring with identity. Let S be a multiplicatively closed set such that 0 ∉ S. Let I be an ideal which is maximal with respect to the condition that
S ⋂ I = Ø.
Which of the following is necessarily true?
1
I is a maximal ideal.
2
I is a prime ideal.
3
I = (1).
4
I = (0).
5
Question Not Attempted