998 Index generate, dependency relation, 338 generator abelian category, 629 cyclic group, 30 generators and relations algebra, 710 group, 280 module, 452 global dimension, left, 949 Going Down Theorem, 907 Going Up Theorem, 906 Goldman, O., 908 Goodwillie, T. G., 743 Gordan, P., 314 graded algebra, 704 graded map, 705 Grassmann algebra, 720 Grassmann, H., 720 greatest common divisor domain, 124 several polynomials, 132 two polynomials, 107 Green’s Theorem, 752 Green, G., 752 Griess, R., 750 Griffith, P. A., 977 Gr¨ obner basis, 380 Gromov, M., 292 Grothendieck group, 859, 861, 863 Jordan–H¨ older, 867 reduced, 862 Grothendieck, A., 857, 866, 870 group abelian, 18 affine, 90 alternating, 29 axioms, 17, 27 Boolean, 19 circle group, 19 cyclic, 29 dicyclic, 284 dihedral, 25 infinite, 293 finitely generated, 281 finitely presented, 281 four-group, 28 free, 272 free abelian, 228 Frobenius, 596 fundamental, 276 Galois, 175 general linear, 20 generalized quaternions, 271 integers mod m, 30 nilpotent, 260 p-group, 69 Pr¨ ufer, 647 projective unimodular, 265 quasicyclic, 647 quaternions, 43 quotient, 49 ring, 391 simple, 71 solvable, 186, 259 special linear, 37 special unitary, 701 symmetric, 5 topological, 520 unitary, 701 unitriangular, 248 group algebra, 392 group object, 436 group of units, 86 group ring, 391 Hall, P., 260, 773 Hamel basis, 323 Hamel, G. K. W., 323 Hamilton, W. R., 43, 393, 662, 849 Hasse, H., 611, 694 Hasse–Minkowski Theorem, 694 height abelian group, 876 prime ideal, 961 height sequence, 876 Heller, A., 870 Herbrand quotient, 847 Herbrand, J., 847 hereditary ring, 934 Hermite, C., 15 hermitian, 701 Herstein, I. N., 601 Higgins, P. J., 286 Higman, D. G., 562 Higman, G., 292, 607 Hilbert, D., 81, 221, 314, 601 Basis Theorem, 315 Nullstellensatz, 356, 914 Theorem 90, 206 Theorem on Syzygies, 960 Hirzebruch, F. E. P., 870 Hochschild, G. P., 858 older, O., 255 Hom functor, 437, 439 homogeneous element, 704 homogeneous ideal, 705 homogeneous resolution, 839 homology, 755 abstract simplicial complex, 755 complex, 785 homology class, 755 homology groups of G, 832 homomorphism R-homomorphism, 398
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