Index 1007 symmetry, 25 symplectic basis, 689 group, 696 syzygy, 946 T.I. set, 600 target, 420 Tarski monsters, 654 Tarski, A., 654 Tartaglia, 1 tensor algebra, 709 tensor product, 470 terminal object, 435 Third Isomorphism Theorem groups, 52 modules, 406 Thompson, J. G., 209, 257, 596, 599 Thrall, R. M., 562 3 × 3 Lemma, 486 Three Subgroups Lemma, 263 top element, 512 topological group, 520 Tor, 802 tor, 802 torsion group, 241 module, 636 subgroup, 241 submodule, 636 torsion-free, 636 totally ordered abelian group, 898 trace, 212, 567, 916 trace form, 917 transcendence basis, 338 transcendence degree, 340 transcendental element, 161 transcendental extension, 331 transfer, 846 transformation of direct system, 509 transition matrix, 150 transitive doubly, 593 group action, 65 transposition, 6 transvection, 264 transversal, 286 Schreier, 289 trivial character, 570 trivial module, 540 type T(X | R), 281 abelian group, 877 pure extension field, 181 UFD, 303 Ulm, H., 237 unique factorization domain, 303 unique factorization, k[x], 111 unit, 86 noncommutative ring, 538 unitary group, 701 matrix, 701 transformation, 701 unitriangular, 248 universal central extension, 836 Universal Coefficients Theorem, 830 universal mapping problem, 425 solution, 425 upper bound, 199 valuation, 898 discrete, 853 valuation ring, 897 discrete, 875 van der Waerden trick, 276 van der Waerden, B. L., 607 van Kampen’s Theorem, 281 van Kampen, E., 281 Vandermonde matrix, 742 Vandermonde, A.-T., 742 variety, 350 irreducible, 358 vector space, 133 Vi` ete, F., 1, 2 Vietoris, L., 795 virtually, 846 virtually small, 860 Vogtmann, K., 292 von Dyck, W., 271 von Neumann regular, 952 von Neumann, J., 952 Watts, C. E., 510 weak dimension, 952 Wedderburn Theorem finite division rings, 531, 607 Wedderburn, J. M., 531, 849 Wedderburn–Artin Theorem semisimple rings, 553, 557 weight, 370 Weir, A. J., 286 well-ordered, 318 Weyl algebra, 534 Weyl, H., 534 Whitehead’s problem, 825 Whitehead, J. H. C., 795 Widman, J., 1 Wielandt, H., 246 Wiles, A., 899 Williams, K. S., 128 Wilson’s Theorem, 37 Wilson, J., 37
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