Noetherian Ring Definition Ideal Definition Characters Determine Representations Representation Theory Pointwise Supremum Preserves Convexity Algebra Monotonicity of Secant Slopes for Convex Functions Algebra Classification of Semisimple Lie Algebras by Cartan Matrix Algebra Unique Maximal Submodule of a Verma Module Lie Algebras Abel–Ruffini–Galois Algebra Roots of Unity Average Lemma Representation Theory Classification of Finite-Dimensional Semisimple Lie Algebras Algebra Algebra Area