# 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.

×