## Algebraic Theories (Google eBook)This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and groups. All topics are developed with a remarkable lucidity and discussed in close connection with their most frequent mathematical applications. 1926 edition. |

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### Contents

Pairs of Bilinear Quadratic and Hennitian Forms | 112 |

First Principles of Groups of Substitutions | 135 |

Fields Reducible and Irreducible Functions | 150 |

Group of an Equation for a Given Field | 159 |

Equations Solvable by Radicals | 178 |

Constructions with Ruler and Compasses | 204 |

Reduction of Equations to Normal Forms | 210 |

### Common terms and phrases

adjunction algebraic alternating group belongs binary form called canonical form coeffi coefficients in F conjugate constant COROLLARY corresponding covariant cyclic group denote distinct edition elementary divisors elements equal equation of degree field F greatest common divisor group for F group G group matrix Hence Hermitian forms Hermitian matrix Hessian homogeneous linear integers invariant factors invariant subgroup irreducible group irreducible in F letters linear functions linear group linear transformation linearly independent Math multiple n-rowed non-singular notation obtain pair of bilinear permutation polynomial prime principal minors proof quadratic forms quantities in F quartic quintic equation quotient rank rational function rational numbers reduced replaces roots of unity rotations seminvariant solvable by radicals solvable group square matrix square root substitution of G symmetric group THEOREM 12 Theorem 9 theory tion trans Unabridged republication unaltered values variables whence write X-matrix

### References to this book

Lie Groups: History, Frontiers and Applications. Hilbert's invariant theory ... DAVID AUTOR HILBERT,Róbert Hermann No preview available - 1978 |