Index 995 differential form, 726 differentials, 622 dihedral group, 25 infinite, 293 dimension, 141, 324 dimension shifting, 797 Diophantus, 899 direct limit, 505 finite, 626 direct product commutative rings, 101 groups, 54 modules, 427 rings, 392 direct sum abelian groups, 224 additive category, 615 complexes, 623 matrices, 656 modules, 427 external, 408, 410 internal, 409, 410 vector spaces, 145, 154 direct summand, 409 direct system, 504 transformation, 509 directed set, 506 Dirichlet, J. P. G. L., 236, 899, 926, 931 discrete valuation ring, 875 discriminant, 212 bilinear form, 686 of OE , 927 of cubic, 213 of quartic, 219 disjoint permutations, 6 disjoint union, 428 divisible module, 464 division algebra, 601 Division Algorithm k[x], 102 k[x1,...,xn], 377 division ring, 393 divisor, 86 Dlab, V., 562 domain commutative ring, 84 DVR, 875 morphism, 420 PID, 127 regular local ring, 975 UFD, 303 Double Centralizer Theorem, 604 doubly transitive, 593 sharply, 595 dual basis, 154 dual space, 154 functor, 440 duals in category, 426 DVR, 875 Dye, R. L., 694 Dynkin diagrams, 749 Dynkin, E., 749 Eckmann, B., 845 Eckmann–Shapiro Lemma, 845 Eick, B., 63 eigenvalue, 659, 660 eigenvector, 659, 660 Eilenberg, S., 418, 460, 871, 935 Eisenstein Criterion, 121 Eisenstein, G., 121 elementary cancellation, 274 elementary divisors finite abelian group, 238 matrix, 666 modules, 644 elementary matrix, 676 elementary symmetric functions, 174 elimination ideal, 388 empty word, 272 endomorphism abelian group, 392 module, 403 ring, 392 Engel’s Theorem, 747 Engel, F., 747 enlargement of coset, 52, 407 enveloping algebra, 484 epimorphism (epic), 617 equivalence class, 34 equivalence relation, 34 equivalent categories, 627 extensions, 770, 818 height sequences, 877 matrices, 672 normal series, 254 representations, 566 series, groups, 254 series, modules, 526 etymology abelian, 209 abelian category, 619 adjoint functors, 514 alternating group, 29 artinian, 552 automorphism, 43 bar resolution, 838 canonical form, 658 commutative diagram, 423 cubic, 93 cycle, 6 dihedral group, 25 domain, 87
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