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 …

We introduce the n-pure projective (resp., injective) dimension of complexes in n-pure
derived categories, and give some criteria for computing these dimensions in terms of the n …

We investigate the properties of pure derived categories of module categories, and show
that pure derived categories share many nice properties of classical derived categories. In …

In this paper, we introduce a class of exact structures in terms of finiteness conditions of
modules, which are called n-pure exact structures. We investigate the properties of n-pure …

Let R be a commutative noetherian local ring. We denote by mod R the category of finitely
generated R-modules, and by Db (R) the bounded derived category of mod R. First, we …

Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

This work clarifies the relationship between the openness of the regular locus of a
commutative Noetherian ring R and the existence of generators for the category of finitely …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

For each $ n\in\mathbb {N}\cup\{\infty\} $, we introduce the notion of $ n $-singularity
category $\mathbf {D} _ {n {\rm-} sg}(R) $ of a given ring $ R $, which can be seen as a …

We introduce the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …