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Unformatted text preview: Proof. Exercises 6.5.1 through 6.5.3 . n This result suggests making the following denitions: Denition 6.5.9. An integral domain R is a principal ideal domain (PID) if every ideal of R is principal. Denition 6.5.10. An integral domain is a unique factorization domain (UFD) if every nonzero element has a factorization by irreducibles that is unique up to order and multiplication by units. According to Theorem 6.5.8 , every Euclidean domain is both a principal ideal domain and a unique factorization domain. The rest of this section will be devoted to a further study of principal ideal domains and unique factorization domains; the main result will be that every principal...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Integers

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