Bound on Character Values Representation Theory Continuous Homomorphisms $\mathbb{R} \to S^1$ Representation Theory Homomorphisms Preserve Identity Group Theory Splitting Lemma for Short Exact Sequences of Modules Algebra Existence of Algebraic Closure Algebra Uniqueness Of Jordan Form Via Nullities Linear Algebra Structure Theorem for Finitely Generated Modules over Euclidean Domains Module Theory Chambers and Positive Systems of a Root System Algebra Algebra Area