Mar 4, 2023 · Let R R (A) (A) denote the nilradical of the commutative ring A A i.e. the ideal containing all nilpotent elements of A A, which is also the intersection of all prime ideals of A A. For A A commutative ring with 1 1, then, R R (A[x]) = ⋂ P prime in A[x] P ⊂ ⋂ p prime in A p[x] (A [x]) = ⋂ P prime in A [x] P ⊂ ⋂ p prime in A p [x] since …