Internal Direct Product Theorem Group Theory Abelian Groups Have One-Dimensional Irreducibles Representation Theory Dual Map Is Linear Linear Algebra Triple Cross Product Identity Vector Algebra Solvability in Degree at Most Four Galois Theory Compatibility of Chain Homotopy with Composition Algebra Chain Homotopic Maps Induce the Same Homomorphism on Homology Algebra Every Module Is a Quotient of a Free Module Algebra Algebra Area