🗺️ Map of Content - Modules

Basic structures

Modules
Module morphisms
Submodules
Module morphisms and submodules

Constructions on modules

Quotient modules
The Isomorphism Theorems for Modules
Direct products of modules
Direct sums of modules
Sums of submodules
Direct products vs. direct sums vs. sums
Free modules
Examples of free modules
Generators for modules and submodules

Bimodules

Bimodules
Bimodule morphisms
The 2-category of bimodules

Tensor products

Tensor Products I - Extending scalars
Tensor Products II - Tensor products of bimodules
Tensor Products III - Balanced Maps and a Universal Property of the Tensor Product
Tensor Products IV - The Adjoint Property

Exact sequences

Exact Sequences I - Illustrative Examples
Exact Sequences II - Exact Sequences
Exact Sequences III - Morphisms of Exact Sequences
Exact Sequences IV - Exact Sequences and Functors

Modules over a PID

Noetherian modules
Linear independence, rank and the structure of free modules
Modules over a PID - The Fundamental Theorem
Rational Canonical Form I - Definition
Rational Canonical Form II - Additional Properties
Rational Canonical Form III - Computation
Jordan Canonical Form I - Definition
Jordan Canonical Form II - Computation