Ring theory MOC

Unique factorization domain

A unique factorization domain or UFD is an integral domain such that every nonzero element has a factorization as a product of irreducible elements, unique up to units and the order of factors. num

Every UFD is also a GCD domain.

Equivalent characterizations

Let be an integral domain. The following are equivalent:

1. is a UFD;
2. Every irreducible element in is prime and satisfies the ^N2 on principal ideals.¹

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develop | en | sembr

Footnotes

1. 2009. Algebra: Chapter 0, § V.2.2, p. 253 ↩