992 Index associativity, 17 generalized, 21, 707 Atiyah, M., 870 augmentation, 549, 832 augmentation ideal, 549, 832 Auslander, M., 562, 751, 950, 955, 977, 981 Auslander–Buchsbaum Theorem, 978, 981 automorphism field, 174 group, 43 inner, outer, 43 automorphism group, 43 Axiom of Choice, 317 Baer sum, 772, 825 Baer, R., 285, 462, 764, 824, 879 bar resolution, 838 normalized, 841 Barr, M., 276 Barratt, M. G., 795 Barratt–Whitehead Theorem, 795 basic subgroup, 653 basis dependency relation, 338 free abelian group, 228 free algebra, 710 free group, 272 free module, 450 ideal, 312 standard, 139 vector space finite-dimensional, 139 infinite-dimensional, 322 Basis Theorem Burnside, 262 finite abelian groups, 234, 467 finitely generated abelian groups, 643 Hilbert, 315 modules, 643 Bass, H., 416, 466, 870 Bautista, R., 562 Beltrami, E., 350 Besche, H. U., 63 biadditive, 469 bidegree, 856 bifunctor, 487 bilinear form, 682 alternating, 683 nondegenerate, 686 skew, 684 symmetric, 683 negative definite, 691 positive definite, 691 bilinear function, 469 bimodule, 445 Binomial Theorem commutative ring, 84 exterior algebra, 722 Bkouche, R., 457 Block, R. E., 748 Boole, G., 19 Boolean group, 19 Boolean ring, 89, 302 Boone, W. W., 291 boundaries, 785 simplicial, 755 boundary map, simplicial, 754 bracelet, 80 bracket, 744, 745 Brady, N., 292 Brauer group, 610 relative, 611 Brauer, R., 562, 584, 608, 611 Brauer–Thrall conjectures, 562 Brussel, E., 849 Buchberger’s algorithm, 385 Buchberger’s Theorem, 383 Buchberger, B., 370, 380 Buchsbaum, D. A., 751, 977, 981 Burnside Basis Theorem, 262 Burnside ring, 590 Burnside’s Lemma, 76, 576 Burnside’s problem, 291 Burnside’s Theorem, 563, 592 Burnside, W., 76, 291 cancellation law domain, 84 group, 18 Cardano, G., 1 Carmichael, R., 270 Carnap, R., 437 Cartan, E., 743, 748 Cartan, H., 935 castle problem, 4 Casus Irreducibilis, 183 categorical statement, 624 category, 419 abelian, 619 additive, 614 cocomplete, 628 composition, 419 G-category, 862 generator, 629 morphism, 419 noetherian, 634 objects, 419 opposite, 441 pre-additive, 422 small, 490 virtually small, 860 Cauchy sequence, 501 Cauchy’s Theorem, 68 Cauchy, A.-L., 4
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