Generator/generators for cyclic group $\mathbb Z[i]/(11-8i)$, given the following isomorphism: [duplicate]
Solution 1:
Here is an answer, based on the discussion in the comments:
The method is correct, but there was a calculation mistake. The correct answer is that the module $V$ is isomorphic to $\mathbb Z[i]/\langle -11 + 8i \rangle.$