infinite, 30, 32–33, 36
isomorphism, 25, 31
of an equation, 23
of permutations, 22–26
of transformations, 28–30
quotient, 25, 34
representation theory, 83, 97–98
simple, 34
sources, 17–22
Group algebra, 43, 97
H
Hamilton, William Rowan (1805–1865), 42,
45, 83, 86, 87, 108, 109, 116, 118,
144–157
Hensel, Kurt (1861–1941), 55, 73, 74
Hermite, Charles (1822–1901), 82, 83
Hilbert, David (1862–1943), 54, 56–59, 66,
74, 93–95, 105, 116,125, 159, 160
Hilbert Basis Theorem, 56, 58, 93, 116
Hilbert Nullstellensatz, 56
Hypercomplex number system, 41–43, 47,
97, 98, 108
I
Ideal, 46, 47, 51, 53, 65, 66, 94–96, 124–126
prime, 51–54, 65, 95, 96
Ideal number, 26, 50–54, 124
Integer, 105, 152
algebraic. See Algebraic integer.
complex, 48
cyclotomic, 48, 52
Gaussian, 49, 65, 105, 106
Invariants, 57–58, 92–94, 115–116, 157, 159
J
Jacobi, Carl Gustav (1804–1851), 49, 83,
156
Jordan, Camille (1838–1921), 25, 26,
29, 34, 83
Jordan canonical form, 83
Jordan-Hölder Theorem, 25, 34
K
Klein, Felix (1849–1925), 20–22, 28–30, 33,
119, 159, 160
Kronecker, Leopold (1823–1891), 27, 28,
50, 51, 67, 68, 81, 83, 132
Kronecker’s Theorem, 67
Kummer, Ernst (1810–1893), 26, 48, 50–54
L
Lagrange, Joseph Louis (1736–1813), 18,
19, 22, 108, 109, 134
Lagrange’s Theorem, 19
Lamé, Gabriel (1795–1870), 48
Laplace, Pierre Simon (1749–1827), 81
Lasker, Emanuel (1868–1941), 56, 59, 94, 98
Lattice, 130
Leibniz, Gottfried (1646–1716), 13, 80, 81,
104
Lie, Sophus (1842–1899), 21, 30, 46, 159
Lie algebra, 45, 46
Lie group, 45, 46
Linear algebra. See Algebra.
Linear associative algebra, 44
Linear equations. See Equation.
Linear independence, 84, 87, 88
Linear transformations, 82, 87, 88, 131
Liouville, Joseph (1809–1882), 50
M
Macauley, Francis (1862–1937), 56, 59, 94
Maclaurin, Colin (1698–1746), 81
Matrices, 43, 81, 82, 97, 117–118
Module, 88, 95–98
N
Newton, Isaac (1642–1727), 11, 13, 119
Noether, Emmy (1882–1935), 54, 59, 60, 88,
91–102, 125, 126, 157–163
legacy, 99–101
Noetherian ring. See Ring.
Notation, 3, 5, 8–10
Number theory, 19, 140–142
algebraic. See Algebraic number theory.
analytic. See Analytic number theory.
Numbers, 104
algebraic. See Algebraic number.
complex, 7–8, 13, 74, 86, 98, 108, 109,
142, 149–150
natural, 123, 128–129
negative, 13, 71, 104
p-adic, 55, 73–74
real, 107, 123, 126–128
O
Octonions, 43, 85, 109, 156
Order, 52
Index 167