Openness of various loci over Noetherian rings

被引：2
|
作者：
Kimura, Kaito [1 ]
机构：
[1] Nagoya Univ, Grad Sch Math, Chikusaku, Nagoya 4648602, Japan
来源：
JOURNAL OF ALGEBRA | 2023年 / 633卷
关键词：
Openness of loci; Nagata criterion; Finite injective dimension; Gorenstein; Cohen-Macaulay; GORENSTEIN;
D O I：
10.1016/j.jalgebra.2023.05.042
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the openness of the P-locus of a finitely generated module over a commutative noetherian ring in the case where P is each of the properties FID, Gor, Can, CM, MCM, (Sn), and (Tn). One of the main results asserts that FID-loci over an acceptable ring are open. We give a module version of the Nagata criterion, and prove that it holds for all of the aforementioned properties.& COPY; 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：403 / 424
页数：22
相关论文
共 50 条
  • [21] MODULES OVER HEREDITARY NOETHERIAN PRIME RINGS
    SINGH, S
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (03): : A389 - A389
  • [22] FINITELY EMBEDDED MODULES OVER NOETHERIAN RINGS
    GINN, SM
    MOSS, PB
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 81 (04) : 709 - 710
  • [23] FI-modules over Noetherian rings
    Church, Thomas
    Ellenberg, Jordan S.
    Farb, Benson
    Nagpal, Rohit
    GEOMETRY & TOPOLOGY, 2014, 18 (05) : 2951 - 2984
  • [24] Modules over hereditary Noetherian prime rings
    Tuganbaev, AA
    RUSSIAN MATHEMATICAL SURVEYS, 2000, 55 (02) : 363 - 364
  • [25] RIGHT NOETHERIAN RINGS INTEGRAL OVER THEIR CENTERS
    BLAIR, WD
    JOURNAL OF ALGEBRA, 1973, 27 (01) : 187 - 198
  • [26] RIGHT NOETHERIAN RINGS INTEGRAL OVER THEIR CENTERS
    WANGNEO, CL
    TEWARI, K
    COMMUNICATIONS IN ALGEBRA, 1979, 7 (15) : 1573 - 1598
  • [27] Persistence of homology over commutative noetherian rings
    Avramov, Luchezar L.
    Iyengar, Srikanth B.
    Nasseh, Saeed
    Sather-Wagstaff, Keri
    JOURNAL OF ALGEBRA, 2022, 610 : 463 - 490
  • [28] FIm-modules over Noetherian rings
    Li, Liping
    Yu, Nina
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, 223 (08) : 3436 - 3460
  • [29] Cotilting modules over commutative Noetherian rings
    Stovicek, Jan
    Trlifaj, Jan
    Herbera, Dolors
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2014, 218 (09) : 1696 - 1711
  • [30] MODULE EXTENSIONS OVER NOETHERIAN-RINGS
    BROWN, KA
    JOURNAL OF ALGEBRA, 1981, 69 (02) : 247 - 260
12345