An upper bound for the dimension of bounded derived categories

Abstract

Let Λ be an artin algebra. We give an upper bound for the dimension of the bounded derived category of the category mod Λ of finitely generated right Λ-modules in terms of the projective and injective dimensions of certain class of simple right Λ-modules as well as the radical layer length of Λ. In addition, we give an upper bound for the dimension of the singularity category of mod Λ in terms of the radical layer length of Λ.