 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/ii/paper-2/21f/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

a

lies in

I \cap J

, then

a \in I \cap J

. Conversely, if

a^{m} \in I

and

a^{n} \in J

a^{m a x (m, n)}

lies in both ideals. Therefore $I \cap J = I \cap J$ for any commutative ring.

 New to topics? Read the docs here!