凝聚环与FP-内射环

PrefaceNotationsChapter 1 A glance in rings and modules1.1 Rings and modules1.2 Complexes, homological dimensions and functors1.3 Finitely generated and finitely presented modules1.4 FP-injective and flat modulesExercise

Chapter 2 Coherent rings2.1 Definition and examples2.2 Characterizations of coherent rings2.3 Extensions of coherent rings2.4 Some generalizationsExercise

Chapter 3 FP-injective rings3.1 Definition and examples3.2 Characterizations of FP-injective rings3.3 Extensions of FP-injective rings3.4 FP-injective and QF rings3.5 FC ringsExercise

Chapter 4 Homological dimensions4.1 FP-injective dimension4.2 n-FC rings4.3 Weak global dimension4.4 Semihereditary ringsExercise

Chapter 5 Some applications5.1 Flat envelopes and FP-injective covers5.2 Gorenstein flat modules5.3 Gorenstein FP-injective modules5.4 Gorenstein flat complexes5.5 Gorenstein FP-injective complexes5.6 Relative and Tate homologyExercise

Appendix A Open questionsAppendix B Categories and fuctorsAppendix C Categories of complexes of modulesReferencesIndex

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《凝聚环与FP-内射环（英文版）》的所要着重讨论的内容之一。