4
$\begingroup$

Show that an integral domain $A$ is a unique factorization domain if and only if every ascending chain of principal ideals terminates, and every irreducible element of $A$ is prime.

  • 2
    Dear Mariam, it is best if you tell us what you have tried and where you are stuck. Otherwise, this feels too much like we are solving problems from a book!2012-05-09
  • 1
    ACCP gives you existence. The other condition gives you uniqueness.2012-05-09

1 Answers 1