Tools of Algebra (1)

Algebra Level 4

Which stament(s) below is/are true?


\(\boxed{1}\).- Every Euclidean domain is an Ideal principal domain and every Ideal principal domain is an Unique factorization domain

\(\boxed{2}\).- Every Ideal principal domain is an Unique Factorization domain and every Unique Factorization domain is an Euclidean domain

\(\boxed{3}\).- Every Unique Factorization domain is an Ideal principal domain and every Ideal principal domain is an Euclidean domain

Bonus.- Give one example or one counter-example in all cases. Of course, if some statement(s) is/are true it will be necessary one wiki for a whole proof. For this reason, I consider sufficent one example or counter- example in every case for the proof.

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