Unique factorization domain

Definition

Symbol-free definition

A commutative unital ring is termed a unique factorization domain if it is an integral domain and every element can be expressed as a product of finite length of irreducible elements (possibly with multiplicity) in a manner that is unique upto the ordering of the elements.

Definition with symbols

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Relation with other properties

Stronger properties

• Euclidean domain
• Principal ideal domain

Weaker properties

• Normal domain: For full proof, refer: UFD implies normal
• gcd domain: For full proof, refer: UFD implies gcd