1002 Index Morita Theory, 631 Morita, K., 631 morphism, 419 epic, 617 identity, 420 monic, 617 Motzkin, T. S., 128 multilinear function, 706 alternating, 717 multiple, 86 multiplication by r, 399 multiplication table, 39 multiplicative subset, 301, 882 multiplicity, 112 Nagata, M., 751 Nakayama’s Lemma, 535 Nakayama, T., 535 natural isomorphism, 488 natural map groups, 50 modules, 406 rings, 156, 396 vector spaces, 155 natural numbers, 29 natural transformation, 488 Navarro, G., 235 N/C Lemma, 67 Neumann, B. H., 607 Neumann, H., 607 Nielsen, J., 285 Nielsen–Schreier Theorem, 289 nilpotent element, 354 group, 260 ideal, 536 Lie algebra, 747 matrix, 670 nilradical, 367, 910 Noether, E., 50, 175, 313, 363, 607, 611 noetherian, 313, 413, 527 category, 634 left, 413 nondegenerate, 686 nonderogatory, 663 nonsingular linear transformation, 145 matrix, 20 nontrivial subgroup, 28 norm, 206, 916 algebraic integer, 163 Euclidean ring, 125 normal basis, 923 extension, 184 primary decomposition, 366 series, 186 factor groups, 186 length, 186 refinement, 254 subgroup, 41 generated by X, 46 maximal, 74 Normal Basis Theorem, 926 normalized bar resolution, 841 normalizer, 66 not-necessarily-associative algebra, 744 Novikov, P. S., 291, 292 nullhomotopic, 787 Nullstellensatz, 356, 914 weak, 355, 914 number field algebraic, 902 cyclotomic, 923 quadratic, 915 O’Brien, E. A., 63 objects of category, 419 obstruction, 814 odd permutation, 12, 13 Ojanguren, M., 866 Ol’shanskii, A. Yu., 292, 654 operation, 16 opposite category, 441 opposite ring, 402 orbit, 64 orbit space, 64 order finitely generated torsion module, 644 group, 25 group element finite, 23 infinite, 23 power series, 95 order ideal, 417, 635 order-reversing, 200 ordered abelian group, 898 totally ordered, 898 orthogonal basis, 690 orthogonal complement, 686 orthogonal direct sum, 688 orthogonal group, 696 Orthogonality Relations, 575 orthonormal basis, 690 outer automorphism, 43 p-adic fractions, 302 p-adic integers, 502 p-adic numbers, 502 p-group, 69, 250 p-primary, 941 p-primary abelian group, 230 (p)-primary module, 641
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