FR-Injective Modules Over Coherent Domains

被引:0
|
作者
Chen, Mingzhao [1 ,2 ]
Qu, Xiaobing [2 ]
Zhao, Wei [1 ,3 ]
机构
[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China
[2] Leshan Normal Univ, Coll Math & Phys, Leshan 614000, Peoples R China
[3] Aba Teachers Univ, Sch Math, Wenchuan 623002, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
Reflexive module; FR-injective module; I-FR-cover; I-FR-envelope; FLAT; RINGS; ENVELOPES; COVERS; DIMENSIONS;
D O I
10.1007/s41980-024-00938-0
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, an R-module M is called FR-injective if Ext(R)(1)(F,M)=0 for every finitely generated reflexive R-module F. We generalize some properties of FP-injective modules to FR-injective modules, consider the relationships between injective modules, FP-injective modules and FR-injective modules, gives some characterizations of (Pi-coherent) rings with property that all finitely generated reflexive modules are projective, and show that a coherent domain is a Prufer domain if and only if it is an 1-FC domain with finite weak global dimension, a coherent domain R is of w.gl.dim(R)<= 2 if and only if every (finitely generated) ideal of R is FR-injective, and a noetherian domain is 2-Gorenstein if and only if R is self FR-injective. Finally, we discuss some properties of I-FR-covers and I-FR-envelopes, where I-FR denotes the class of all FR-injective modules.
引用
收藏
页数:20
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