Let R be a commutative noetherian ring and M a finitely generated R-module. In this paper,
we reconstruct M from its Koszul homology with respect to a suitable sequence of elements …

Let R be a commutative Noetherian ring and I be an ideal of R such that the R-modules HI i
(M) are I-cofinite, for all finitely generated R-modules M and all i∈ ℕ 0. In this paper, we …

This is the first of a series of four papers describing the finitely generated modules over all
commutative noetherian rings that do not have wild representation type (with a possible …

In this paper, we prove a version of Freyd's generating hypothesis for triangulated
categories: if D is a cocomplete triangulated category and S∈ D is an object whose …

We consider the bounded derived category D b (R mod) of a left Noetherian ring R. We give
a version of the Generalized Auslander–Reiten Condition for D b (R mod) that is equivalent …

It is known that if R is a ring with identity, and S and A op are the functor rings associated to
the categories Mod (R) and Mod (R op), respectively, then there is a duality between the …

Let R be a commutative Noetherian ring and I be an ideal of R. In this article, we answer
affirmatively a question raised by the present author. Also, as a consequence, it is shown …

Let C be a subcategory of the category of finitely generated R-modules over a commutative
noetheian ring R. We prove that, if C is closed under images and extensions (which we call …

1. Introduction Page 1 TAIWANESE JOURNAL OF MATHEMATICS Vol. 20, No. 5, pp. 1001–1008,
October 2016 DOI: 10.11650/tjm.20.2016.7324 This paper is available online at http://journal.tms.org.tw …

Let (S, n) be a commutative noetherian local ring and ω∈ n be non-zerodivisor. This paper
deals with the behavior of the category Mon (ω, P) consisting of all monomorphisms …