Journal of the
Korean Mathematical Society JKMS

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 length 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, module categories

MSC numbers: Primary 18G20, 16E10, 18E10

Supported by: This work was financially supported by NSFC (11971225, 11901341) and the NSF of Shandong Province (ZR2019QA015)