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Question
Suppose that R is a unique factorization domain and that a,b ∈R are distinct irreducible elements. Which of the following statements is TRUE?
Options:
A .  The ideal 〈1+a〉 is a prime ideal
B .  The ideal 〈a+b〉 is a prime ideal
C .  The ideal 〈1+ab〉 is a prime ideal
D .  The ideal 〈a〉 is not necessarily a maximal ideal
Answer: Option D


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