凝聚环和FP 内射环 英文版PDF电子书下载

Notations 1

Chapter 1 A glance in rings and modules 1

1.1 Rings and modules 1

1.2 Complexes,homological dimensions and functors 17

1.3 Finitely generated and finitely presented modules 23

1.4 FP-injective and fiat modules 28

Exercise 47

Chapter 2 Coherent rings 52

2.1 Definition and examples 52

2.2 Characterizations of coherent rings 54

2.3 Extensions of coherent rings 70

2.4 Some generalizations 78

Exercise 91

Chapter 3 FP-injective rings 96

3.1 Definition and examples 96

3.2 Characterizations of FP-injective rings 97

3.3 Extensions of FP-injective rings 106

3.4 FP-injective and QF rings 116

3.5 FC rings 121

Exercise 134

Chapter 4 Homological dimensions 138

4.1 FP-injective dimension 138

4.2 n-FC rings 149

4.3 Weak global dimension 153

4.4 Semihereditary rings 164

Exercise 170

Chapter 5 Some applications 174

5.1 Flat envelopes and FP-injective covers 174

5.2 Gorenstein flat modules 187

5.3 Gorenstein FP-injective modules 202

5.4 Gorenstein flat complexes 214

5.5 Gorenstein FP-injective complexes 222

5.6 Relative and Tate homology 231

Exercise 251

Appendix A Open questions 258

Appendix B Categories and fuctors 263

Appendix C Categories of complexes of modules 275

References 284

Index 303