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- Prove that the ideal <x2 + 1> is prime in Z[x] but not maximal in Z[x]. Be clear, detailed. Give math rules, theorems, etc. Be legible.Prove that {0R} is not a prime ideal in Z12.Explain why (or prove) {∑nk=3 akxk|ak ∈ R} is not a prime ideal in R[x].In a principal ideal domain, show that every nontrivial prime idealis a maximal ideal.
- Please help with this question :Let p element of Z be prime . Show that PZ is a maximal ideal . Note if it reaches 12h30 pls don't answerExplain why 3Z is not an ideal in Q. What is the difference between the notation <3> and {3} .What is the difference between the notation <3,4> and <3> ∪ <4> .Consider the ideal {0,2,4,6,8,10} of Z12. Which of these elements generate the ideal?
