Commutative rings in which every ideal is a product of primary ideals
The authors characterize the commutative rings with identity in which every ideal is a finite product of primary ideals. They call a ring with this property a Q-ring. They show that R is a Q-ring if and only if R is Laskerian (every ideal in R has a primary decomposition) and every nonmaximal prime ideal of R is finitely generated and locally principal. They prove that the polynomial ring R[X] or the formal power series ring \(RX\) is a Q-ring if and only if R is a general ZPI-ring, that is, R is a finite direct product of Dedekind domains and special principal ideal rings.
scientific article; zbMATH DE number 3981304