Naoyuki Matsuoka

activity

20062026

most citedOn the almost Gorenstein property in Rees algebras of contracted ideals

11 citations · 47 across the 22 of their papers we have counts for

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25 papers · 1 filter

math.AC2026

Traces of powers of canonical ideals

Le Truong Hoang, Naoyuki Matsuoka

Let $(R,\m)$ be a one-dimensional Cohen--Macaulay local ring with a canonical fractional ideal $R \subseteq K \subseteq R$ , and let $v$ denote its embedding dimension. Put $…

math.AC2026

The structure of almost symmetric almost complete intersection numerical semigroups

Kazufumi Eto, Naoyuki Matsuoka, Alessio Moscariello +3

We prove a structure theorem for numerical semigroups H that are almost symmetric and almost complete intersections. We show that a row-factorization (RF) matrix of H must possess…

math.AC2026

Normality of ideals beyond the standard graded setting: families from numerical semigroup rings

Naoyuki Matsuoka

Let $k$ be an arbitrary field and let $S = k [x, y, z]$ be the polynomial ring with three variables $x, y, z$ . We study integrally closed $(x, y, z)$ -primary ideals of $S$ that are homogene…

math.AC2026

Normality of monomial ideals in three variables

Maki Ataka, Naoyuki Matsuoka

An ideal $I$ in a Noetherian ring is called \textit{normal} if $I^{n}$ is integrally closed for all $n \geq 1$ . Zariski proved that in two-dimensional regular local rings, every inte…

math.AC2025

Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings

Do Van Kien, Naoyuki Matsuoka, Taiga Ozaki

The pseudo-Frobenius numbers of a numerical semigroup $H$ are deeply connected to the structure of the defining ideal of its semigroup ring $k [H]$ . In this paper, we resolve a cert…

math.AC2024

Almost Gorenstein simplicial semigroup rings

Kazufumi Eto, Naoyuki Matsuoka, Takahiro Numata +1

We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to…

math.AC2023

Nearly Gorenstein local rings defined by maximal minors of a $2 \times n$ matrix

Shinya Kumashiro, Naoyuki Matsuoka, Taiga Nakashima

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,…

math.AC2023

Remarks on almost Gorenstein rings

Naoki Endo, Naoyuki Matsuoka

This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $…

math.AC2022

On the weakly Arf $(S_{2})$ -ifications of Noetherian rings

Naoki Endo, Shiro Goto, Shin-ichiro Iai +1

The weakly Arf $(S_{2})$ -ification of a commutative Noetherian ring $R$ is considered to be a birational extension which is good next to the normalization. The weakly Arf property (W…

math.AC2021

When are the rings $I : I$ Gorenstein?

Naoki Endo, Shiro Goto, Shin-ichiro Iai +1

Let $I (\neq = A)$ be an ideal of a $d$ -dimensional Noetherian local ring $A$ with $ht_{A} I \geq 2$ , containing a non-zerodivisor. The problem of when the ring $I:I=\oper…

math.AC2021

Ulrich ideals in the ring $k [[t^{5}, t^{11}]]$

Naoki Endo, Shiro Goto, Shin-ichiro Iai +1

The Ulrich ideals in the semigroup rings $k [[t^{5}, t^{11}]]$ and $k [[t^{5}, t^{6}, t^{9}]]$ are determined, by describing the normal forms of systems of generators, where $k [[t]]$ denotes t…

math.AC2020

On the ubiquity of Arf rings

Ela Celikbas, Olgur Celikbas, Cătălin Ciupercă +4

We introduce and develop the theory of weakly Arf rings, which is a generalization of Arf rings, initially defined by J. Lipman in 1971. We provide characterizations of weakly Arf…

math.AC2019

Efficient generation of ideals in core subalgebras of the polynomial ring k[t] over a field k

Naoki Endo, Shiro Goto, Naoyuki Matsuoka +1

This note aims at finding explicit and efficient generation of ideals in subalgebras $R$ of the polynomial ring $S = k [t]$ ( $k$ a field) such that $t^{c_{0}} S \subseteq R$ for some int…

math.AC2017★ 1 cited

Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings

Shiro Goto, Do Van Kien, Naoyuki Matsuoka +1

The structure of the defining ideal of the semigroup ring $k [H]$ of a numerical semigroup $H$ over a field $k$ is described, when the pseudo-Frobenius numbers of $H$ are multiples…

math.AC2017★ 11 cited

Sally modules of canonical ideals in dimension one and 2-AGL rings

Tran Do Minh Chau, Shiro Goto, Shinya Kumashiro +1

The notion of 2-AGL ring in dimension one which is a natural generalization of almost Gorenstein local ring is posed in terms of the rank of Sally modules of canonical ideals. The…

math.AC2016★ 10 cited

Almost Gorenstein Rees algebras of $p_{g}$ -ideals, good ideals, and powers of the maximal ideals

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi +1

Let $(A, m)$ be a Cohen-Macaulay local ring and let $I$ be an ideal of $A$ . We prove that the Rees algebra $R (I)$ is an almost Gorenstein ring in the followin…

math.AC2016★ 11 cited

On the almost Gorenstein property in Rees algebras of contracted ideals

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi +1

The question of when the Rees algebra $R (I) = ⨁_{n \geq 0} I^{n}$ of $I$ is an almost Gorenstein graded ring is explored, where $R$ is a two-dimensional regular loca…

math.AC2015

The almost Gorenstein Rees algebras of parameters

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi +1

There is given a characterization for the Rees algebras of parameters in a Gorenstein local ring to be almost Gorenstein graded rings. A characterization is also given for the Rees…

math.AC2015★ 3 cited

The almost Gorenstein Rees algebras over two-dimensional regular local rings

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi +1

Let $(R, m)$ be a two-dimensional regular local ring with infinite residue class field. Then the Rees algebra $R (I) = ⨁_{n \geq 0} I^{n}$ of $I$ is an almos…

math.AC2014★ 2 cited

Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes

Naoyuki Matsuoka, Satoshi Murai

In this paper, we study simplicial complexes whose Stanley-Reisner rings are almost Gorenstein and have $a$ -invariant zero. We call such a simplicial complex an almost Gorenstein*…

math.AC2011★ 4 cited

Almost Gorenstein rings

Shiro Goto, Naoyuki Matsuoka, Tran Thi Phuong

The notion of almost Gorenstein ring given by Barucci and Fr{ö}berg \cite{BF} in the case where the local rings are analytically unramified is generalized, so that it works well al…

math.AC2008

On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves

Kazuhiko Kurano, Naoyuki Matsuoka

In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal of the space monomial curves $(t^{a}, t^{b}, t^{c})$ for pairwise coprime integers $a$ , $b$ ,…

math.AC2007

Quasi-socle ideals in local rings with Gorenstein tangent cones

Shiro Goto, Satou Kimura, Naoyuki Matsuoka +1

Quasi-socle ideals, that is the ideals $I$ of the form $I = Q : m^{q}$ in a Noetherian local ring $(A, m)$ with the Gorenstein tangent cone $\mathrm{G}(\mathfrak…

math.AC2007★ 2 cited

Quasi-socle ideals in Gorenstein numerical semigroup rings

Shiro Goto, Satoru Kimura, Naoyuki Matsuoka

Quasi-socle ideals, that is the ideals $I$ of the form $I = Q : m^{q}$ in Gorenstein numerical semigroup rings over fields are explored, where $Q$ is a parameter ideal, and…

Traces of powers of canonical ideals

The structure of almost symmetric almost complete intersection numerical semigroups

Normality of ideals beyond the standard graded setting: families from numerical semigroup rings

Normality of monomial ideals in three variables

Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings

Almost Gorenstein simplicial semigroup rings

Nearly Gorenstein local rings defined by maximal minors of a 2×n matrix

Remarks on almost Gorenstein rings

On the weakly Arf (S2​)-ifications of Noetherian rings

When are the rings I:I Gorenstein?

Ulrich ideals in the ring k[[t5,t11]]

On the ubiquity of Arf rings

Efficient generation of ideals in core subalgebras of the polynomial ring k[t] over a field k

Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings

Sally modules of canonical ideals in dimension one and 2-AGL rings

Almost Gorenstein Rees algebras of pg​-ideals, good ideals, and powers of the maximal ideals

On the almost Gorenstein property in Rees algebras of contracted ideals

The almost Gorenstein Rees algebras of parameters

The almost Gorenstein Rees algebras over two-dimensional regular local rings

Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes

Almost Gorenstein rings

On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves

Quasi-socle ideals in local rings with Gorenstein tangent cones

Quasi-socle ideals in Gorenstein numerical semigroup rings

Nearly Gorenstein local rings defined by maximal minors of a $2 \times n$ matrix

On the weakly Arf $(S_{2})$ -ifications of Noetherian rings

When are the rings $I : I$ Gorenstein?

Ulrich ideals in the ring $k [[t^{5}, t^{11}]]$

Almost Gorenstein Rees algebras of $p_{g}$ -ideals, good ideals, and powers of the maximal ideals