Introduction to Modules (Algebra 2) – UC Irvine Graduate Algebra Lectures
by Nathan Kaplan · UC Irvine (YouTube: nckaplan math)
A 20-video lecture playlist from Nathan Kaplan's UC Irvine graduate algebra course (Math 206B/230B). It covers module definitions, submodules, homomorphisms, quotient modules, direct sums, free modules, and exact sequences in short 10–15 minute segments.
More resources on Modules
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Stack Exchange - Modules Tag
Questions and answers on Mathematics Stack Exchange tagged for modules over rings: submodules, quotients, homomorphisms, exact sequences, tensor products and free and projective modules. Useful for checking exercise solutions and seeing how standard module-theory arguments are written.
Module Theory: An Approach to Linear Algebra (Electronic Edition)
Free CC BY 4.0 edition of T. S. Blyth's textbook, revised from the 1990 Oxford second edition. It builds modules from the basics through exact sequences, tensor products, free and projective modules, and modules over a PID, then canonical forms.
Modules over a PID
Keith Conrad's expository proof of the structure theorem for finitely generated modules over a principal ideal domain. It covers submodules of free modules, the invariant factor and elementary divisor forms, and applications to finite abelian groups and linear operators.
Algebra: Chapter 0
A graduate-level algebra text that uses category theory from the start to treat groups, rings, modules, fields and linear algebra in one framework, then continues to homological algebra. Readers learn to work with universal properties, exact sequences and Ext/Tor.