This book examines the notions of dimension and decomposition for module categories. It discusses some basic properties of quasidecomposition functions and the complete lattice of all quasidecomposition functions taking values in a fixed given lattice.
1. Quasidecomposition functions
2. Assassin functions
3. Radical functions
4. Associated ideal functions
5. The function
6. Coirreducible modules
7. Decompositions
8. Quasidimension functions
9. The function
10. Relations between quasidecomposition functions and quasidimension functions
11. Linearization of quasidecomposition and quasidimension functions
12. Gabriel dimension
13. Torsion-theoretic Krull dimension
14. GRK-dimension
15. Classical Krull dimension
Jonathan S. Golan
