J. Korean Math. Soc. 2020; 57(6): 1389-1406
Online first article June 3, 2020 Printed November 1, 2020
https://doi.org/10.4134/JKMS.j190681
Copyright © The Korean Mathematical Society.
Yeyang Peng, Tiwei Zhao
Nanjing University; Qufu Normal University
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)
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