The derived and extension dimensions of abelian categories

Abstract

For an abelian category $\mathcal{A}$, 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.

Journal of Algebra, 606 (2022), 243--265

References in corpus (3)

• Rejective subcategories of artin algebras and orders
• The Extension Dimension of Abelian Categories
• Derived dimensions of representation-finite algebras