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 fiat 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