996 Index exact sequence, 727 Ext, 818 exterior algebra, 716 factor set, 766 field, 87 flat, 493 free group, 280 functor, 437 homology, 752 homomorphism, 38 ideal, 900 isomorphism, 38 K-Theory, 870 kernel, 40 left exact, 444 nilpotent, 748 polyhedron, 25 power, 20 pure subgroup, 231 quadratic, 93 quasicyclic, 647 quaternions, 393 quotient group, 49 radical, 353 rational canonical form, 658 ring, 81 symplectic, 689 syzygy, 946, 951 Tor, 830 torsion subgroup, 241 transvection, 264 variety, 350 vector, 134 Euclid’s Lemma, 109, 125, 127 Euclidean Algorithm, k[x], 110 Euclidean ring, 124 Euler φ-function, 31 Euler Theorem, 36 Euler, L., 130, 899 Euler–Poincar´ e characteristic, 795 evaluation homomorphism, 97 even permutation, 12 exact abelian category, 619 functor, 445, 624 left, 443 right, 476 hexagon, 847 sequence, 411 complexes, 788 factored, 417 short, 412 splice, 418 triangle, 792 Exchange Axiom, 337 Exchange Lemma, 142 exponent group, 239 module, 645 Ext, 809 ext, 811 extension central, 836 universal, 836 groups, 256, 757 modules, 412, 818 of ideal, 903 extension field, 160 algebraic, 161 degree, 160 finite, 160 Galois, 197, 521 normal, 184 pure, 181 purely inseparable, 347 purely transcendental, 335 radical, 181 separable, 176 simple, 203 exterior algebra, 716 exterior derivative, 726 exterior power, 716 factor groups, 186 factor modules, 526 factor set, 766 factorial ring (see UFD), 303 faithful G-set, 593 faithful module, 402 Feit, W., 209, 257 Feit–Thompson Theorem, 209 Fermat’s Theorem, 36 Fermat, P., 899 FFR, 960 Fibonacci, 743 field, 87 algebraic closure, 327 algebraically closed, 327 finite, 180 fraction, 88 perfect, 343 rational functions, 93 15-puzzle, 12, 14 filtration, 854 finite extension, 160 limit, 626 order (module), 635 topology, 520 finite-dimensional, 137 finitely generated group, 281 ideal, 312
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