Nakayama's Lemma Algebra Cayley-Hamilton for Modules Algebra Root Space Decomposition for Semisimple Lie Algebras Algebra Abelian Groups Have One-Dimensional Irreducibles Representation Theory Spectral Theorem for Hermitian Matrices Linear Algebra Element Order Divides Group Order Group Theory Sign Homomorphism Group Theory Modules over Noetherian Rings Algebra Algebra Area