Index Abel, N. H., 4, 209 abelian category, 619 abelian group, 18 divisible, 464 free abelian, 228 ordered, 898 primary, 230 rank 1, 874 reduced, 647 torsion, 241, 636 torsion-free, 636 totally ordered, 898 abelian Lie algebra, 745 absolute Galois group, 524 abstract simplicial complex, 753 ACC, 312, 527 Accessory Irrationalities, 191 action of group, 64 transitive, 65 acyclic, 786 additive category, 614 additive functor, 441, 614 adjoining a unit, 89 adjoining to field, 161 adjoint determinants, 737 linear transformation, 695, 701 adjoint functors, 514 Adjoint Isomorphism, 491, 492 Ado, I. D., 746 Adyan, S. I., 292 aﬃne group, 90, 595 afforded by, 568 Albert, A. A., 611, 849 algebra, 482 central simple, 601 crossed product, 850 cyclic, 850 division, 601 enveloping, 484 graded, 704 not-necessarily-associative, 744 algebra map, 482 algebraic closure, 327 element, 161 extension, 161 integer, 117, 902, 915 conjugate, 163 number field, 902 numbers, 326 algebraically closed, 327 dependent, 335 almost all, 322 alternating bilinear form, 683 group, 29 multilinear, 717 space, 683 Amitsur, S. A., 601, 714, 849 annihilator, 537, 635, 967 anti-isomorphism, 403 Arf invariant, 694 Arf, C., 694 Artin, E., 175, 552 Artin, M., 882 artinian ring, 527 ascending chain condition, 312 associated prime ideal, 364 associated reduced polynomial, 213 associates, 100 991

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