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 …

This thesis is comprised of three chapters. The first chapter deals with bounded complexes
of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative …

Nihonkai Math. J. Vol.22(2011), 67–71 ON THE CATEGORY OF COFINITE MODULES FOR
PRINCIPAL IDEALS 1. Introduction Page 1 Nihonkai Math. J. Vol.22(2011), 67–71 ON THE …

Throughout this note, we shall use the same notation as in [6] 1 and assume that all rings
are commutative and noetherian with identity (see [1] and [6] for the definitions needed in …

Let $\mathfrak {a} $ be a proper ideal of a commutative noetherian ring $ R $ and $ d $ a
positive integer. We answer Hartshorne's question on cofinite complexes completely in the …

Remark that the concept of J-cofiniteness for complexes does not always agree with that for
modules. On the other hand, if N is an A-module and J-cofinite, then N• is a J-cofinite …

Let A be a homomorphic image of a Gorenstein ring of finite Krull dimension, J an ideal of A
of dimension one, and N• a bounded-below complex of A-modules. Suppose that A is …

The category of cofinite modules for ideals of dimension one and codimension one Page 1
Troisième Rencontre Internationale sur les Polynômes à Valeurs Entières Rencontre …

Our aim in this paper is to introduce the results on the Betti numbers of local cohomology
modules, which are obtained from the recent results on a category of cofinite modules …

This report is the announcement of the result on the characterization of cofinite complexes
(the first one is in the talk at the RIMS conferencet). Let A be a homomorphic image of a …