A History of Algebra: From al-Khwārizmī to Emmy Noether

abelian group al-Khwarizmi Annalen basis elements called Cardano Cartan Cayley Chapter characters coefficients commutative completely reducible complex numbers cubic equation Dardi's Dedekind defined Descartes determinant direct sum divisor double tangents Élie Cartan Emmy Noether entitled equal equation of degree Euclid Euler factor finite groups Frobenius Galois group Gauss geometry given ground field group algebra group G group of substitutions Gruppen hence Hermann Weyl Hölder ideal integer invariant irreducible representations isomorphic Jordan Lagrange Leonardo letter Lie algebra Lie groups line segments linear transformations Math mathematics memoir method modulo Molien multiplication number field obtains Oeuvres Omar orthogonal paper permutations plane polynomial prime problem proof proved published quadratic equation quaternions quintic equation radicals rational functions ring rotations says semi-simple solution solvable solved Sophus Lie square subalgebra subgroup Tabit theorem Traité translation treatise variables vector Viète Weyl x₁ zero