Index 993 Cayley Theorem, 60 Cayley, A., 28, 60, 62 Cayley–Hamilton Theorem, 662 center group, 42 Lie algebra, 750 matrix ring, 154, 415 ring, 394 centerless, 42 central extension, 836 universal, 836 central simple algebra, 601 centralizer group element, 66 subgroup, 66 subset of algebra, 604 chain, 317 of complex, 785 simplicial, 754 chain map, 622 over f, 800 change of rings, 449 character, 193, 568 afforded by, 568 degree, 568 generalized, 573 induced, 580 irreducible, 568 kernel, 577 linear, 568 regular, 570 restriction, 584 table, 573 trivial, 570 character group, 495 characteristic of field, 158 polynomial, 660 sequence, 673 subgroup, 250 chessboard, 80 Chevalley, C., 743, 854 Ch’in Chiu-shao, 4 Chinese Remainder Theorem k[x], 170 commutative rings, 301 circle operation, 90 circle group, 19 Claborn, L., 931 class equation, 69 function, 570 group, 931 number, 931 sums, 559 Classification Theorem of Finite Simple Groups, 257, 269 Clifford algebra, 728 Clifford, W. K., 728 closed under operation, 17 coboundary, 769 cocomplete, 628 cocycle identity, 766 codiagonal, 616, 824 cofactor, 738 cofinal subset, 321 Cohen, I. S., 320, 904 Cohn, P. M., 934 cohomological dimension, 844 cohomology group, 770 cohomology groups of G, 832 coinduced module, 848 cokernel additive category, 618 modules, 406 Cole, F., 267 colimit (see direct limit), 505 colon ideal, 302 coloring, 78 column space of matrix, 155 common divisor several polynomials, 132 two polynomials, 107 commutative, 18 commutative diagram, 423 commutative ring, 83 Boolean, 89 Dedekind, 927 domain, 84 DVR, 875 Euclidean ring, 124 field, 87 integers in number field, 902 Jacobson, 912 local, 302 regular, 973 noetherian, 313 p-adic fractions, 302 PID, 127 polynomial ring, 91 several variables, 94 reduced, 354 UFD, 303 valuation ring, 897 commutator, 257 subgroup, 257 companion matrix, 657 Comparison Theorem, 798 complement of subgroup, 761 complete factorization, 9 completely reducible, 565 completion, 502 complex, 622 abstract simplicial, 753

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