Shin-ichiro Iai

activity

20212024

most citedGorensteinness in Rees algebras of powers of parameter ideals

1 citations · 1 across the 4 of their papers we have counts for

collaborators

5 papers

math.AC2024

Some characterizations of Gorenstein Rees Algebras

Shin-ichiro Iai

The aim of this paper is to elucidate the relationship between the Gorenstein Rees algebra $R (I) := ⨁_{i \geq 0} I^{i}$ of an ideal $I$ in a complete Noetherian local ring $A$ an…

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★ 1 cited

Gorensteinness in Rees algebras of powers of parameter ideals

Shiro Goto, Shin-ichiro Iai

This paper gives a necessary and sufficient condition for Gorensteinness in Rees algebras of the $d$ -th power of parameter ideals in certain Noetherian local rings of dimension $d\…

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…

Some characterizations of Gorenstein Rees Algebras

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

When are the rings I:I Gorenstein?

Gorensteinness in Rees algebras of powers of parameter ideals

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

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

When are the rings $I : I$ Gorenstein?

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