Threading Homology through Algebra Selected Patterns [Hardcover]

Threading Homology through Algebratakes homological themes (Koszul complexes and their variations, resolutions in general) and shows how these affect the perception of certain problems in selected parts of algebra, as well as their success in solving a number of them. The text deals with regular local rings, depth-sensitive complexes, finite free resolutions, letter-place algebra, Schur and Weyl modules, Weyl-Schur complexes and determinantal ideals. Aimed at graduates and academics in mathematics, the book provides an overview of the developments that have taken place in these areas as well as an insight into some of the open problems which exist.

Preface
1. Recollections and Perspectives
2. Local Ring Theory
3. Generalized Koszul Complexes
4. Structure Theorems for Finite Free Resolutions
5. Exactness Criteria at Work
6. Weyl and Schur Modules
7. Some Applications of Weyl and Schur Modules
Appendix for Letter-place Methods
References
Index