Author(s): L.R. Vermani
Publisher: Chapman & Hall
Year: 2003
Title page
Preface
1 Modules
1.1 Modules
1.2 Free Modules
1.3 Exact Sequences
1.4 Homomorphisms
1.5 Tensor Product of Modules
1.6 Direct and Inverse Limits
1.7 Pull Back and Push Out
2 Categories and Functors
2.1 Categories
2.2 Functors
2.3 The Functors Hom and Tensor
3 Projective and Injective Modules
3.1 Projective Modules
3.2 Injective Modules
3.3 Baer's Criterion
3.4 An Embedding Theorem
4 Homology of Complexes
4.1 Ker-Coker Sequence
4.2 Connecting Homomorphism - the General Case
4.3 Homotopy
5 Derived Functors
5.1 Projective Resolutions
5.2 Injective Resolutions
5.3 Derived Functors
6 Torsion and Extension Functors
6.1 Derived Functors-Revisited
6.2 Torsion and Extension Functors
6.3 Some Further Properties of Tor^R_n
6.4 Tor and Direct Limits
7 The Functor Ext_R^n
7.1 Ext^l and Extensions
7.2 Baer Sum of Extensions
7.3 Some Further Properties of Ext_R^n
8 Hereditary and Semihereditary Rings
8.1 Hereditary Rings and Dedekind Domains
8.2 Invertible Ideals and Dedekind Rings
8.3 Semihereditary and Prüfer Rings
9 Universal Coefficient Theorem
9.1 Universal Coefficient Theorem for Homology
9.2 Universal Coefficient Theorem for Cohomology
9.3 The Künneth Formula - a Special Case
10 Dimensions of Modules and Rings
10.1 Projectively and Injectively Equivalent Modules
10.2 Dimensions of Modules and Rings
10.3 Global Dimension of Rings
10.4 Global Dimension of Noetherian Rings
10.5 Global Dimension of Artin Rings
11 Cohomology of Groups
11.1 Homology and Cohomology Groups
11.2 Some Examples
11.3 The Groups H⁰(G,A) and H₀(G,A)
11.4 The Groups H^l(G,A) and H_l(G,A)
11.5 Homology and Cohomology of Direct Sums
11.6 The Bar Resolution
11.7 Second Cohomology Group and Extensions
11.8 Some Homomorphisms
11.9 Some Exact Sequences
12 Some Applications
12.1 An Exact Sequence
12.2 Outer Automorphisms of p-groups
12.3 A Theorem of Magnus
Bibliography
