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.
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页码：403 / 424
页数：22
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