The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.
What type of commutative ring does the Lasker–Noether theorem express every ideal as an intersection of primary ideals in?
a Noetherian commutative ring