The derived dimensions and syzygy finite type

Abstract

Let $\Lambda$ be an artin algebra, and $\mathcal{V}$ a subset of all simple modules in $\mathrm{mod}\Lambda$. Suppose that $Λ/\rad Λ$ has finite syzygy type, then the derived dimension of $\Lambda$ is at most $\ell\ell^{t_{\mathcal{V}}}(Λ_Λ)+\pd\mathcal{V}.$ In particular, if the global dimension of $\Lambda$ is finite, then the derived dimension of $\Lambda$ is at most $\ell\ell^{t_{\mathcal{V}}}(Λ_Λ)+\pd\mathcal{V}.$ This generalized the famous result which state that the derived dimension of $\Lambda$ is less than or equal to the global dimension of $\Lambda$.

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References in corpus (1)

• Derived dimensions of representation-finite algebras