Assignment:
Q1. Give a example of a commutative ring that has a maximal ideal that is not a prime ideal.
Q2. Prove that I = < 2 + 2i> is not a prime ideal of Z[i]. How many elements are in Z[i] / I. What is the characteristic of Z[i] / I.
Provide complete and step by step solution for the question and show calculations and use formulas.