IAAWA Factorization in Integral Domains

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Chapter 6 Factorization in Integral Domains

The building blocks of the integers are the prime numbers. If $F$ is a field, then irreducible polynomials in $F[x]$ play a role that is very similar to that of the prime numbers in the ring of integers. Moreover, as we saw, the proofs used in the two cases, beginning with a division algorithm, and the proving results about the greatest common divisor and unique factorization. Just as the definition of a ring abstracted the properties we'd seen in many examples of rings, we now look for properties in arbitrary integral domains which are similar to the properties of factorization in integers and polynomial rings.