Product ideal

Unique factorization of ideals

A commutative ring 𝑅 admits unique factorization of ideals or UFI iff every nonzero proper ideal 𝐼 ◃𝑅 may be written uniquely (up to ordering) as the product of prime ideals #m/def/ring i.e. there is a bijection between ideals I and multisets ℕP0 of prime ideals.

Rings with UFI

• A Dedekind domain admits UFI

#state/tidy | #lang/en | #SemBr