Hereditary Semi-Primary Rings and Tri-Angular Matrix Rings

Abstract

It is well known that the semi-simple rings with minimum conditions coincide with the rings of global homological dimension zero and that the hereditary rings coincide with the rings of global dimension one. Eilenberg, Jans, Nagao and Nakayama gave some properties of hereditary rings in [4] and [11], which relate to global dimension of factor rings. As an example of non-commutative hereditary ring we know a tri-angular matrix ring over a semi-simple ring.