14 citations · 19 across the 17 of their papers we have counts for
20 papers
Almost Gorenstein standard graded rings and their localizations
Naoki Endo
We prove that a Cohen-Macaulay standard graded integral domain over a field is almost Gorenstein as a graded ring if and only if the completion of its localization at the graded ma…
Nearly Gorenstein blow-up algebras over two-dimensional regular local rings
Naoki Endo, Ken-ichi Yoshida
In this paper, we slightly extend the framework of nearly Gorenstein graded rings introduced by Herzog-Hibi-Stamate, and investigate the nearly Gorenstein property of the blow-up a…
Modules of minimal multiplicity over one-dimensional Cohen-Macaulay local rings
Ela Celikbas, Olgur Celikbas, Naoki Endo +1
We study finitely generated modules of minimal multiplicity, a notion introduced by Puthenpurakal that extends the classical concept of minimal multiplicity from rings to modules.…
Normality of Ideals and Modules
Naoki Endo, Shiro Goto, Jooyoun Hong +1
We investigate when the Rees algebra of an integrally closed -primary ideal in a regular local ring is a Cohen-Macaulay normal domain. While this property always hold…
Quasi-Gorenstein extended Rees algebras associated with filtrations
Naoki Endo
This paper investigates the quasi-Gorenstein property of extended Rees algebras associated with the Hilbert filtrations on a Noetherian local ring. We provide necessary and suffici…
Goto rings
Naoki Endo
As part of stratification of Cohen-Macaulay rings, we introduce and develop the theory of Goto rings, generalizing the notion of almost Gorenstein rings originally defined by V. Ba…
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 is an almost Gorenstein graded ring, the localization $…
How many ideals whose quotient rings are Gorenstein exist?
Naoki Endo
For an Ulrich ideal in a Gorenstein local ring, the quotient ring is again Gorenstein. Aiming to further develop the theory of Ulrich ideals, this paper investigates a naive questi…
Reflexive modules over the endomorphism algebras of reflexive trace ideals
Naoki Endo, Shiro Goto
In the present paper we investigate reflexive modules over the endomorphism algebras of reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem gene…
On the weakly Arf -ifications of Noetherian rings
Naoki Endo, Shiro Goto, Shin-ichiro Iai +1
The weakly Arf -ification of a commutative Noetherian ring is considered to be a birational extension which is good next to the normalization. The weakly Arf property (W…
When are the rings Gorenstein?
Naoki Endo, Shiro Goto, Shin-ichiro Iai +1
Let be an ideal of a -dimensional Noetherian local ring with , containing a non-zerodivisor. The problem of when the ring $I:I=\oper…
A criterion for reflexivity of modules
Naoki Endo, Shiro Goto
Let be a finitely generated module over a ring . With certain mild assumptions on , it is proven that is a reflexive -module, once as a -module…
Ulrich ideals in the ring
Naoki Endo, Shiro Goto, Shin-ichiro Iai +1
The Ulrich ideals in the semigroup rings and are determined, by describing the normal forms of systems of generators, where denotes t…
Ulrich ideals in numerical semigroup rings of small multiplicity
Naoki Endo, Shiro Goto
Ulrich ideals in numerical semigroup rings of small multiplicity are studied. If the semigroups are three-generated but not symmetric, the semigroup rings are Golod, since the Bett…
Almost Gorenstein determinantal rings of symmetric matrices
Ela Celikbas, Naoki Endo, Jai Laxmi +1
We provide a characterization of the almost Gorenstein property of determinantal rings of a symmetric matrix of indeterminates over an infinite field. We give an explicit formula f…
Topics on strict closure of rings
Naoki Endo, Shiro Goto, Ryotaro Isobe
In 1971, J. Lipman introduced the notion of strict closure of a ring in another, and established the underlying theory in connection with a conjecture of O. Zariski. In this paper,…
Construction of strictly closed rings
Naoki Endo, Shiro Goto
The notion of strict closedness of rings was given by J. Lipman in connection with a conjecture of O. Zariski. The present purpose is to give a practical method of construction of…
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…
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 of the polynomial ring ( a field) such that for some int…
Almost Gorenstein rings arising from fiber products
Naoki Endo, Shiro Goto, Ryotaro Isobe
The purpose of this paper is, as part of the stratification of Cohen-Macaulay rings, to investigate the question of when the fiber products are almost Gorenstein rings. We show tha…