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Prove that is not a prime ideal of Z[i]. How many elements

Chapter 14, Problem 38E

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QUESTION:

Prove that \(I= \langle 2+2i \rangle\) is not a prime ideal of Z[i]. How many elements are in Z[i]/I? What is the characteristic of Z[i]/I?

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QUESTION:

Prove that \(I= \langle 2+2i \rangle\) is not a prime ideal of Z[i]. How many elements are in Z[i]/I? What is the characteristic of Z[i]/I?

ANSWER:

Step 1 of 5

The objective is to show that  is not a prime ideal of .

Find the number of elements in  and the characteristic of

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