Index 999 algebra, 482 commutative ring, 96 graded algebra, 705 group, 38 conjugation, 42 natural map, 50 Lie algebra, 746 monoid, 272 ring, 395 semigroup, 272 homotopic, 787 homotopy, contracting, 787 Hopf’s formula, 836 Hopf, H., 832 Hopkins, C., 544 Hopkins–Levitzki Theorem, 544 Houston, E., 208 Hume, J., 1 Hurewicz, W., 411, 832 hyperbolic plane, 688 hypersurface, 352 IBN, 451 ideal, 99, 395 augmentation, 549 basis, 312 colon, 302 commutative ring, 99 elimination, 388 finitely generated, 312 generated by U, 312 homogeneous, 705 invertible, 929 left, 395 Lie algebra, 746 maximal, 298 minimal, 528 monomial, 385 order, 635 primary, 361 prime, 296 principal, 100 proper, 99 radical, 353 right, 395 two-sided, 395 idempotent, 571 identity functor, 437 group element, 17 morphism, 420 image abelian category, 619 linear transformation, 146 module homomorphism, 405 ring homomorphism, 395 increasing p n list, 719 indecomposable, 260 Independence of Characters, 193 independent list, 138 dependency relation, 338 maximal, 143 indeterminate, 92 index of subgroup, 35 induced character, 580 class function, 582 map, 437, 439 homology, 787 module, 580, 848 representation, 580 inductive limit (see direct limit), 505 infinite order, 23, 635 infinite-dimensional, 137 inflation, 846 initial object, 435 injections coproduct, 423, 428 direct sum of modules, 408 injective dimension, 948 module, 460 object in additive category, 618 resolution, 783 injectively equivalent, 949 inner automorphism, 43 inner product, 682 matrix, 684 space, 682 inseparability degree, 347 inseparable extension, 176 inseparable polynomial, 176 integers mod m, 30 integers, algebraic number field, 902 integral basis, 921 closure, 902 element, 900 extension, 900 integrally closed, 902 intermediate field, 197 Invariance of Dimension, 141, 143 invariant (of group), 40 invariant basis number, 451 invariant factors finite abelian group, 239 matrix, 658 modules, 645 invariant subspace, 404 inverse Galois problem, 221 inverse limit, 500 finite, 626 inverse system, 499 inverse, commutative ring, 86
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