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Suppose that in the ring Z, the ideal is a proper ideal of

Chapter 14, Problem 18E

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QUESTION:

Suppose that in the ring Z, the idealis a proper ideal of and is a proper ideal of I. What are the possibilities for J? What are the possibilities for I?

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QUESTION:

Suppose that in the ring Z, the idealis a proper ideal of and is a proper ideal of I. What are the possibilities for J? What are the possibilities for I?

ANSWER:

Step 1 of 2

Since all the ideals of  are of the form . It is known that if and only if . So, the ideals that contain are and.

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