A generalization of quasi-hereditary rings

摘要

We give a generalization of quasi-hereditary rings called QH-1 rings. We show that a left QH-1 ring R is quasi hereditary if and only if R has finite global dimension if and only if R has Cartan determinant +1. We then give a bound on the global dimension of the quasi-hereditary serial rings, and charac terize the QH-1 serial rings of infinite global dimension in termi of the admissible sequence.