# Linear Algebra over a Ring

Linear Algebra over a Ring

## Table of Contents Edit

- Modules and linear functions
- The lattice of submodules
- Free modules and matrices
- Direct product, direct sum and tensor product
- Homomorphism and dual modules
- Algebrae over a ring
- Determinants
- Modules over Bézout domains
- Modules over principal ideal domains
- Vector spaces
- Multilinear algebra
- Projective and injective modules
- Torsion
- Flat modules
- Finitely generated modules
- Chain complexes of finitely generated free modules
- The universal coefficient theorems in homology and cohomology