Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Kumashiro, Shinya"'
Autor:
Abdolmaleki, Reza, Kumashiro, Shinya
Let $A$ be a commutative Noetherian local ring with maximal ideal $\mathfrak{m}$, and let $I$ be an ideal. The fiber cone is then an image of the polynomial ring over the residue field $A/\mathfrak{m}$. The kernel of this map is called the defining i
Externí odkaz:
http://arxiv.org/abs/2405.18041
This article investigates the traces of certain modules over rings of invariants associated with finite groups. More precisely, we provide a formula for computing the traces of arbitrary semi-invariants, thereby contributing to the understanding of t
Externí odkaz:
http://arxiv.org/abs/2312.00983
We investigate the nearly Gorenstein property of a local ring defined by the maximal minors of a specific $2 \times n$ matrix with entries in the formal power series ring $k[[X_1, X_2, \ldots , X_n]]$ over a field $k$. Our findings allow us to presen
Externí odkaz:
http://arxiv.org/abs/2308.04234
Autor:
Goto, Shiro, Kumashiro, Shinya
In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a Cohen-Macaulay loc
Externí odkaz:
http://arxiv.org/abs/2212.12762
It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten condition (ARC). In this paper we explore (SAC) along with the several ca
Externí odkaz:
http://arxiv.org/abs/2209.12718
We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. In this paper, we provide characterizations of a Cohen-Macaulay local ring in terms of the sectional genera, the Cohen-Macaulay type, and the second
Externí odkaz:
http://arxiv.org/abs/2206.04859
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 ideals. We also explore properties of such rings related to birationa
Externí odkaz:
http://arxiv.org/abs/2203.04469
Autor:
Herzog, Jürgen, Kumashiro, Shinya
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 Kobayashi.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2201.12508
Autor:
An, Tran Nguyen, Kumashiro, Shinya
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 multiplicity.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2109.00726
Autor:
Kumashiro, Shinya
In this paper, we study Noetherian local rings $R$ having a finite number of trace ideals. We proved that such rings are of dimension at most two. Furthermore, if the integral closure of $R/H$, where $H$ is the zeroth local cohomology, is equi-dimens
Externí odkaz:
http://arxiv.org/abs/2108.00414