11 citations · 32 across the 32 of their papers we have counts for
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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…
When are trace ideals finite?
Shinya Kumashiro
In this paper, we study Noetherian local rings having a finite number of trace ideals. We proved that such rings are of dimension at most two. Furthermore, if the integral clos…
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…
Reflexive modules over Arf local rings
Ryotaro Isobe, Shinya Kumashiro
We provide a certain direct-sum decomposition of reflexive modules over (one-dimensional) Arf local rings. We also see the equivalence of three notions, say, integrally closed idea…