Given a commutative ring R and finitely generated ideal I, one can consider the classes of I-
adically complete, L 0 I-complete and derived I-complete complexes. Under a mild …

Let a be an ideal of a commutative Noetherian (not necessarily local) ring R. In the case cd
(a, R)≤ 1, we show that the subcategory of a-cofinite R-modules is Abelian. Using this fact …

In this paper, we examine the class of K-absolutely pure complexes. These are the
complexes which are right orthogonal in the homotopy category K (R) to the acyclic …

Let X be a chain complex over a commutative noetherian ring R, that is, an object in the
derived category 𝒟 (R). We investigate the small support and co-support of X, introduced by …

Let x _ denote a system of elements of a commutative ring R. For an R-module M we
investigate when x _ is M-pro-regular resp. M-weakly pro-regular as generalizations of M …

We show that the homotopy category of complexes K (B) over any finitely accessible additive
category B is locally well generated. That is, any localizing subcategory L in K (B) which is …

We present an in-depth exploration of the module structures of local (co) homology modules
(moreover, for complexes) over the completion R ̑ 𝔞 R^a of a commutative noetherian ring …

Let R be a commutative noetherian ring and I an ideal of R. Assume that for all integers i the
local cohomology module HI i (R) is I-cofinite. Suppose that R p is a regular local ring for all …

It is well known [i] that simplicial sets provide a convenient combinatorial analog of cellular
topological cell spaces. We recall [2] that a simplicial set is a graded set {Xn}, ne N, such that …

Let I and J be two ideals of a commutative ring R. We introduce the concepts of the C ˇ ech
complex and C ˇ ech cocomplex with respect to (I, J) and investigate their homological …