Ideal Definition Ring Definition Zorn's Lemma Theorem #1226 Matrix Characterisation of Bilinear Rank Algebra Non Degeneracy And Invertibility Linear Algebra Symmetry of the Trace Pairing Algebra Bound on the Galois Group Algebra Injective Iff Trivial Kernel Group Theory Spectral Properties of Hermitian Matrices Linear Algebra Integral Closure of an Ideal as Radical Algebra Dimension Preservation Under Integral Extensions Algebra Algebra Area