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 On the Extension Dimension of Module Categories J. Korean Math. Soc.Published online June 3, 2020 Yeyang Peng and Tiwei Zhao Nanjing University, Qufu Normal University Abstract : Let $\Lambda$ be an artin algebra and $\mod \Lambda$ the category of finitely generated right $\Lambda$-modules. We prove that the radical layer length of $\Lambda$ is an upper bound for the radical layer of $\mod \Lambda$. We give an upper bound for the extension dimension of $\mod \Lambda$ in terms of the injective dimension of a certain class of simple right $\Lambda$-modules and the radical layer length of $D\Lambda$. Keywords : Extension dimension, radical layer length, Abelian Categories MSC numbers : 18G20, 16E10, 18E10 Full-Text :