An Upper Bound for the Dimension of Bounded Derived Categories

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 $Λ$.

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