Noetherian intersections of regular local rings of dimension two

被引：3

作者：

Heinzer, William ^{[1
]}

Olberding, Bruce ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] New Mexico State Univ, Dept Math Sci, Las Cruces, NM 88003 USA

来源：

JOURNAL OF ALGEBRA | 2020年 / 559卷

关键词：

Regular local ring; Quadratic transform; Quadratic tree; Noetherian ring; Complete ideal; Projective model; OVERRINGS; IDEALS;

D O I：

10.1016/j.jalgebra.2020.14.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let D be a 2-dimensional regular local ring and let Q(D) denote the quadratic tree of 2-dimensional regular local overrings of D. We describe the desingularization of projective models over D both algebraically in terms of the saturation of complete ideals and order-theoretically in terms of the quadratic tree Q(D). We prove that this describes all the Noetherian rings that are intersections of rings in Q(D). (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：320 / 345

页数：26

共 50 条

[21] Characterizations of regular local rings in positive characteristics
Li, Jinjia
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (05) : 1553 - 1558
[22] SIMPLE VALUATION IDEALS OF ORDER 3 IN TWO-DIMENSIONAL REGULAR LOCAL RINGS
Noh, Sunsook
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 23 (04): : 511 - 528
[23] The almost Gorenstein Rees algebras over two-dimensional regular local rings
Goto, Shiro
Matsuoka, Naoyuki
Taniguchi, Naoki
Yoshida, Ken-ichi
JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (10) : 3425 - 3436
[24] On the Finiteness Properties of Local Cohomology Modules for Regular Local Rings
Sedghi, Monireh
Bahmanpour, Kamal
Naghipour, Reza
TOKYO JOURNAL OF MATHEMATICS, 2017, 40 (01) : 83 - 96
[25] NOETHERIAN SPECTRUM ON RINGS AND MODULES
Rush, David E.
GLASGOW MATHEMATICAL JOURNAL, 2011, 53 : 707 - 715
[26] Noetherian completion and PI rings
Amiram Braun
Israel Journal of Mathematics, 2015, 209 : 487 - 506
[27] The α-invariant and Gorensteinness of graded rings associated to filtrations of ideal in regular local rings
Goto, S
Hayasaka, F
Iai, S
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (01) : 87 - 94
[28] Bounds on Dao numbers and applications to regular local rings
Ficarra, Antonino
Miranda-Neto, Cleto B.
Queiroz, Douglas S.
ANNALI DI MATEMATICA PURA ED APPLICATA, 2024,
[29] Superstability, noetherian rings and pure-semisimple rings
Mazari-Armida, Marcos
ANNALS OF PURE AND APPLIED LOGIC, 2021, 172 (03)
[30] Some aspects in Noetherian modules and rings
Zeyada, Nasr Anwer
Makki, Makkiah S.
AIMS MATHEMATICS, 2022, 7 (09): : 17019 - 17025

← 1 2 3 4 5 →