13 papers
The set of trace ideals of curve singularities
Toshinori Kobayashi, Shinya Kumashiro
This paper mainly focuses on commutative local domains of dimension one. We then obtain a criterion for a ring to have a finite number of trace ideals in terms of integrally closed…
Upper bound on the colength of the trace of the canonical module in dimension one
Jürgen Herzog, Shinya Kumashiro
We study the upper bound of the colength of trace of the canonical module in one-dimensional Cohen-Macaulay rings. We answer the two questions posed by Herzog-Hibi-Stamate and Koba…
The irreducible multiplicity and Ulrich modules
Tran Nguyen An, Shinya Kumashiro
In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible mu…
The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one
Jürgen Herzog, Shinya Kumashiro, Dumitru I. Stamate
We study one-dimensional Cohen-Macaulay rings whose trace ideal of the canonical module is as small as possible. In this paper we call such rings far-flung Gorenstein rings. We inv…
Integrally closed ideals of reduction number three
Shinya Kumashiro
In a Cohen-Macaulay local ring , we study the Hilbert function of an integrally closed -primary ideal whose reduction number is three. With a m…
Graded filtrations and ideals of reduction number two
Shinya Kumashiro
In this paper, we give a way to construct graded filtrations of graded modules. We then apply it to the Sally module, which describes a correction term of the Hilbert function. As…