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.
$A$ is a unique factorization domain iff $A$ satisfies the ACCP and irreducibles are prime
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abstract-algebra
ring-theory
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2Dear 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
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1ACCP gives you existence. The other condition gives you uniqueness. – 2012-05-09