It is shown that, given any left artinian ring Λ which has vanishing radical cube and n
isomorphism classes of simple left modules, the global dimension of Λ is either infinite or …

Setting Let A be a left artinian ring with J"= 0, where J is the Jacobson radical of A. Given a
left A-module M, we will denote the projective dimension of M by p dim M, or by p dim, M if …