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If R and S are principal ideal domains, prove that R S is
Chapter 14, Problem 43E(choose chapter or problem)
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:
Questions & Answers
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 .