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