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
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