ABSTRACT

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.

chapter Chapter 0|28 pages

Notation, Terminology, and Background Information

chapter Chapter 1|11 pages

Quasidecomposition Functions

chapter Chapter 2|4 pages

Assassin Functions

chapter Chapter 3|8 pages

Radical Functions

chapter Chapter 4|8 pages

Associated Ideal Functions

chapter Chapter 5|8 pages

The Function δ

chapter Chapter 6|20 pages

Coirreducible Modules

chapter Chapter 7|7 pages

Decompositions

chapter Chapter 8|9 pages

Quasidimension Functions

chapter Chapter 9|3 pages

The Function ε

chapter Chapter 12|12 pages

Gabriel Dimension

chapter Chapter 13|9 pages

Torsion-Theoretic Krull Dimension

chapter Chapter 14|19 pages

GRK-Dimension

chapter Chapter 15|6 pages

Classical Krull Dimension