On pure derived and pure singularity categories
K-Theory and Homology
2020-09-10 v1 Rings and Algebras
Abstract
Firstly, we compare the bounded derived categories with respect to the pure-exact and the usual exact structures, and describe bounded derived category by pure-projective modules, under a fairly strong assumption on the ring. Then, we study Verdier quotient of bounded pure derived category modulo the bounded homotopy category of pure-projective modules, which is called a pure singularity category since we show that it reflects the finiteness of pure-global dimension of rings. Moreover, invariance of pure singularity in a recollement of bounded pure derived categories is studied.
Cite
@article{arxiv.1905.02329,
title = {On pure derived and pure singularity categories},
author = {Tianya Cao and Wei Ren},
journal= {arXiv preprint arXiv:1905.02329},
year = {2020}
}
Comments
Accepted for publication in Journal of Algebra and its Applications. Comments are welcomed!