Non-Vanishing Trace for Separable Extensions Galois Theory Prime Power Class Size Implies Non-Simplicity Representation Theory Subfield Correspondence Algebra Irreducible Representations of $\operatorname{SO}(4)$ Representation Theory Hilbert's Nullstellensatz Algebra Characterisation of Separable Extensions Algebra Properties of the Canonical Projection Group Theory Dimension Theorem Linear Algebra Algebra Area