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If R and S are principal ideal domains, prove that R S is

Chapter 14, Problem 43E

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QUESTION:

If R and S are principal ideal domains, prove that R ? S is a principal ideal ring. (See Exercise 41 for the definition.)Reference:

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QUESTION:

If R and S are principal ideal domains, prove that R ? S is a principal ideal ring. (See Exercise 41 for the definition.)Reference:

ANSWER:

Step 1 of 3

Let's take any ideal  of  and examine its restrictions on component rings  and . Namely, we are interested in sets  and .

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