60 citations · 392 across the 111 of their papers we have counts for
6 papers · 1 filter
Quasi-socle ideals in a Gorenstein local ring
Shiro Goto, Naoyuki Matsuoka, Ryo Takahashi
This paper explores the structure of quasi-socle ideals I=Q:m^2 in a Gorenstein local ring A, where Q is a parameter ideal and m is the maximal ideal in A. The purpose is to answer…
A characterization of modules locally of finite injective dimension
Ryo Takahashi
In this note, finite modules locally of finite injective dimension over commutative Noetherian rings are characterized in terms of vanishing of Ext modules.
An uncountably infinite number of indecomposable totally reflexive modules
Ryo Takahashi
A few years ago, Huneke and Leuschke proved a theorem which solved a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type…
On the number of indecomposable totally reflexive modules
Ryo Takahashi
In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive…
A new approximation theory which unifies spherical and Cohen-Macaulay approximations
Ryo Takahashi
This paper gives a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies two famous approximation theorems; one is due to Ausland…
Totally reflexive modules constructed from smooth projective curves of genus g \geq 2
Ryo Takahashi, Kei-ichi Watanabe
In this paper, from an arbitrary smooth projective curve of genus at least two, we construct a non-Gorenstein Cohen-Macaulay normal domain and a nonfree totally reflexive module ov…