Module Definition Principal Ideal Domain Definition Submodule Definition Rank Definition Rational Formal Power Series Are Algebraic Algebra Universal Property of the Verma Module for a Fixed Borel Subalgebra Lie Algebras UFDs Are Integrally Closed Algebra Eisenstein's Criterion Ring Theory Existence of Eigenvectors over an Algebraically Closed Field Algebra Linearity of Ordinary Generating Functions Algebra Verma Module Character Formula Lie Algebras Orbit-Stabiliser Theorem Group Theory Algebra Area