|
凝聚环与FP-内射环 本书特色
凝聚环源于chase[45]在1960年对平坦模的直积的研究。这一概念可以看成noether环和半遗传环的推广。1989年，glaz编著的《交换的凝聚环》[160]一书出版了。这本由陈建龙、张小向著的《凝聚环与fp-内射环(英文版)》综合了当时人们所知道的有关交换的凝聚环方面的几乎所有的结果。
三年以后，glaz又写了一篇关于交换的凝聚环的综述报告，介绍了凝聚环在交换代数中的地位。与此同时，关于非交换的凝聚环的研究也逐渐活跃起来。这正是本书的所要着重讨论的内容之一。
凝聚环与FP-内射环 目录
preface
notations
chapter 1 a glance in rings and modules
1.1 rings and modules
1.2 complexes, homological dimensions and functors
1.3 finitely generated and finitely presented modules
1.4 fp-injective and flat modules
exercise
chapter 2 coherent rings
2.1 definition and examples
2.2 characterizations of coherent rings
2.3 extensions of coherent rings
2.4 some generalizations
exercise
chapter 3 fp-injective rings
3.1 definition and examples
3.2 characterizations of fp-injective rings
3.3 extensions of fp-injective rings
3.4 fp-injective and qf rings
3.5 fc rings
exercise
chapter 4 homological dimensions
4.1 fp-injective dimension
4.2 n-fc rings
4.3 weak global dimension
4.4 semihereditary rings
exercise
chapter 5 some applications
5.1 flat envelopes and fp-injective covers
5.2 gorenstein flat modules
5.3 gorenstein fp-injective modules
5.4 gorenstein flat complexes
5.5 gorenstein fp-injective complexes
5.6 relative and tate homology
exercise
appendix a open questions
appendix b categories and fuctors
appendix c categories of complexes of modules
references
index
|
