 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-2/9e/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The class

a

is nilpotent exactly when

ϕ (a) = 0

p

makes

a^{e}

p^{e}

. Conversely, the image of a nilpotent in the field

R / (p)

is nilpotent and therefore zero.

 New to topics? Read the docs here!