Abstract Algebra: Theory and Applications, Chapter 11: Homomorphisms
by Thomas W. Judson Β· judsonbooks.org (PreTeXt edition)
Free open-textbook chapter defining group homomorphisms, kernels and images, then proving the First, Second and Correspondence isomorphism theorems. Includes reading questions, exercises, and additional exercises on automorphisms.
More resources on Homomorphisms
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.
nLab: Homomorphism
Wiki entry defining homomorphisms as structure-preserving maps between algebraic structures and relating them to morphisms in a category, with links to monomorphisms, isomorphisms, and related notions. Suits readers who already know basic algebra and want the categorical framing.
Abstract Algebra
Learn abstract algebra homomorphisms with Prof. Benedict Gross! Explore key concepts in this insightful course.
The First Isomorphism Theorem, Intuitively
Short blog post explaining why G/ker Ο is isomorphic to the image of Ο. It groups domain elements into cosets according to where they land, then ties that picture to the commutative-diagram statement of the theorem. The theorem students most often get stuck on; the post gives the standard intuition in a few minutes, as a companion to the Judson chapter.
Visual Algebra, Chapter 4: Maps Between Groups (Lectures 4.1β4.11)
The clearest visual account of what a homomorphism does: every homomorphism as 'quotient by the kernel, then relabel', with a dedicated chapter on the isomorphism theorems. Eleven recorded lectures (about 6.5 hours) with slides, explaining homomorphisms through Cayley diagrams: embeddings and quotients, the fundamental homomorphism theorem, the correspondence and diamond theorems, subquotients and automorphisms. Lectures 8.4β8.5 cover ring homomorphisms.