Integral domain in which any two irreducible factorizations are equal upto ordering and associates
This article defines a property of integral domains, viz., a property that, given any integral domain, is either true or false for that.
View other properties of integral domains | View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions
An integral domain in which any two irreducible factorizations are equal upto ordering and associates is an integral domain satisfying the property that for any element, any two factorizations of that element as products of irreducible elements must be equal upto ordering and associates.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Euclidean domain||click here|
|principal ideal domain||every ideal is principal||click here|
|unique factorization domain||click here|
|Bezout domain||every finitely generated ideal in it is principal||click here|
|integral domain in which every irreducible is prime||Every irreducible is prime implies any two irreducible factorizations are equal upto ordering and associates||click here|