Linear Algebra over a Ring

Ring of integers

Linear Algebra over a Ring

Table of Contents

• 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