Algebra I – autumn 2024 – Homework 11
1. Prove that
I = {a + bi
√
13; a, b ∈ Z, a + 3b is divisible by 22}
is an ideal of Z[i
√
13] = {a + bi
√
13 ∈ C; a, b ∈ Z}.
2. Decide whether I is a prime ideal of Z[i
√
13].
3. Decide whether I is a maximal ideal of Z[i
√
13].