We investigate the endomorphism algebras of finite dimensional modules having the property that every indecomposable finite dimensional -module is of projective dimension at most one or injective dimension at most one. In particular, we describe all matrix algebras with this homological property.
"On endomorphism algebras with small homological dimensions." J. Math. Soc. Japan 54 (3) 621 - 648, July, 2002. https://doi.org/10.2969/jmsj/1191593912