Lying Over Algebra Equivalent Characterisations of Injective Modules Algebra Unique Expansion of Positive Roots in Simple Roots Algebra Localization Is Tensor Product Algebra Thompson's Nilpotency Theorem Representation Theory Characterisations Of Diagonalisability Linear Algebra Principal Ideal Domains Are Unique Factorization Domains Ring Theory Burnside's $p^a q^b$ Theorem Representation Theory Algebra Area