Commutative rings with absorbing factorization

摘要

We use the concept ofn-absorbing ideal introduced by Badawi to study commutative rings having absorbing factorization. To this end, we introduce and investigate the AF-dimension of a ringR- the minimum positive integernsuch thatRhasn-absorbing factorization. We show that the Krull dimension of a finite AF-dimensional ring is at most one and also present several applications.