Restricted left principal ideal rings

A ring is an LD-ring ifR is left bounded, ifR/J is a left Artinian left principal ideal ring for every proper idealJ inR, and ifR has finite left Goldie dimension. IfR is non-Artinian thenR is an order in a simple Artinian ringS. The ideal theory of LD-rings is investigated, and we discuss some conditions under which an LD-ring is an hereditary ring, and some under which an LD-ring is a Noetherian, bounded, maximal Asano order. A central localization of an LD-ring is an LD-ring, and the center of some LD-rings is a Krull-domain. This research was supported in part by the National Science Foundation Grant GP 23861.