1004 Index subgroup, 28 submodule, 404 subspace, 135 Pr¨ ufer, H., 647 Pr¨ ufer group, 647 pullback, 431 pure extension, 181 subgroup, 231 submodule, 652 purely inseparable, 347, 746 purely transcendental, 335 pushout, 432 quadratic field, 915 quadratic form, 692 quadratic polynomial, 93 quartic polynomial, 93, 183 resolvent cubic, 3 quasi-ordered set, 421 quasicyclic group, 647 quaternions, 43 division ring, 393 generalized, 271 Quillen, D., 456, 870 quintic polynomial, 93 quotient complex, 788 Division Algorithm k[x], 103 group, 49 Lie algebra, 747 module, 406 ring, 156 space, 145 r-cycle, 6 R-homomorphism, 398 R-isomorphism, 399 R-linear combination, 405 R-map, 398 R-module, 396 R-sequence, 966 Rabinowitch trick, 355 radical extension, 181 radical ideal, 353 radical of ideal, 353 Rado, R., 236 rank, 873 free abelian group, 229 free group, 278 free module, 451 linear transformation, 155 matrix, 155 rational canonical form, 658 rational functions, 93 Razmyslov, Yu. P., 714 realizes the operators, 761 Recorde, R., 1 reduced abelian group, 647 reduced basis, 387 reduced degree, 343 reduced mod {g1, . . . , gm}, 377 reduced polynomial, 213 reduced ring, 354 reduced word, 273 reduction, 274, 376 Rees, D., 958, 963 refinement, 254, 526 regular character, 570 regular G-set, 595 regular local ring, 973 regular on module, 957 regular representation, 565 Reiten, I., 562 relative Brauer group, 611 relatively prime Z, 31 k[x], 109 UFD, 306 remainder k[x], 103 k[x1,...,xn], 378 mod G, 378 repeated roots, 114 representable functor, 493 representation character, 568 completely reducible, 565 group, 539 irreducible, 559, 565 linear, 565 regular, 565 ring, 401 representation on cosets, 61 representative of coset, 33 residually finite, 279 residue field, 970 resolution bar, 838 normalized, 841 deleted, 798 flat, 950 free, 782 homogeneous, 839 injective, 783 projective, 782 resolvent cubic, 3, 219 restriction cohomology, 846 representation, 584 resultant, 214 retract, 409 retraction, 293, 409 right R-module, 396
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