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

  • The ideal 〈1+a〉 is a prime ideal
  • The ideal 〈a+b〉 is a prime ideal
  • The ideal 〈1+ab〉 is a prime ideal
  • The ideal 〈a〉 is not necessarily a maximal ideal

Answer is "The ideal <a> is not necessarily a maximal ideal"

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169
Vivek

how did the answer came

180
Andrew

please anyone explain this answer

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