Index 1005 right derived functors contravariant, 811 covariant, 808 right exact functor, 478 ring, 81 artinian, 527 Boolean, 302 commutative, 83 division ring, 393 quaternions, 393 endomorphism ring, 392 factorial, 303 group algebra, 392 group ring, 391 hereditary, 934 Jacobson, 912 left noetherian, 527 local, 302 opposite, 402 polynomial, 91 quotient, 156 semisimple, 542, 553 simple, 549 unique factorization domain, 981 von Neumann regular, 952 zero, 82 ring extension, 900 finitely generated, 908 Ringel, C., 562 Roiter, A. V., 562 root of unity, 19, 119 primitive, 119 root, multiplicity, 112 root, polynomial, 104 Rosset, S., 262, 714 Rotman, J. J., 457, 881 roulette wheel, 80 Ruffini, P., 4 Russell’s paradox, 418 Russell, B. A. W., 418 Salmer´ on, L., 562 Sarges, H., 315 asiada, E., 431 saturated, 898 scalar matrix, 153 multiplication, 133 module, 396 transformation, 153 scalar-closed, 966 Schanuel’s Lemma, 457 dual, 467 Schanuel, S. H., 870 Schering, E., 243 Schmidt, O. Yu., 261 Schreier Refinement Theorem groups, 254 modules, 526 Schreier transversal, 289 Schreier, O., 285 Schur’s Lemma, 550, 590 Schur, I., 773 Scipio del Ferro, 1 Second Isomorphism Theorem groups, 52 modules, 406 secondary matrices, 682 Seidenberg, A., 904 self-adjoint, 700 semidirect product, 760 semigroup, 22 homomorphism, 272 semisimple Jacobson, 534 module, 540 ring, 542, 553 separability degree, 347 separable element, 176 extension, 176 polynomial, 176 series, 525 composition, 526 equivalent, 526 factor modules, 526 length, 526 refinement, 526 Serre, J.-P., 286, 456, 751, 858 Serre–Auslander–Buchsbaum Theorem, 977 set, 419 sgn, 13 Shafarevich, I., 221 Shapiro’s Lemma (see Eckmann–Shapiro Lemma), 845 Shapiro, A., 845 Shelah, S., 825 short exact sequence, 412 split, 412 shuffle, 724 signature, 692 signum, 13 similar matrices, 153 Simmons, G. J., 168 simple extension, 203 group, 71 Lie algebra, 747 module, 407 ring, 549 transcendental extension, 331 simple components, 552 simplex, 753
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