The derived and extension dimensions of abelian categories

For an abelian category A, we establish the relation between its derived and extension dimensions. Then for an artin algebra Lambda, we give the upper bounds of the extension dimension of Lambda in terms of the radical layer length of Lambda and certain relative projective (or injective) dimension of some simple Lambda-modules, from which some new upper bounds of the derived dimension of Lambda are induced.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This article investigates the relation between dimensions in an abelian category and an Artin algebra. The upper bounds of the extension dimension and derived dimension of the algebra are provided, based on the radical layer length and relative projective (or injective) dimension of certain simple modules.