356 INDEX ramified, 52, 268, 280 unramified, 19, 41, 45, 46, 48, 49, 53–57, 172, 268, 283, 316 Ann, 242 anti-diagonal block matrix, 159, 235 antichain, 27, 47 apparently split, 109 approximation, 211, 212, 215 Approximation Theorem, 187 AR, see Auslander-Reiten Arnol d, Vladimir I., 260 Artin, Michael, 97, 100, 104, 119, 160 Artin-Rees Lemma, 8 Artinian localization, 17 Artinian pair, 21, 28, 29, 32, 32–39, 42–50, 246, 248, 252, 257, 283 Artinian ring, 5–6, 27, 29, 30, 32, 39, 120, 166, 173, 200, 238, 267, 281, 294 ascent of bounded CM type, 279, 298 of excellence, 167 of finite CM type, 48, 133, 138, 164, 165, 168, 169, 171 associated graded ring, 143, 160, 200 associativity formula, 315 asymmetry, 57, 224 atom, 13, 22 Auslander transpose Tr, 204, 203–223, 238, 239, 281 Auslander, Maurice, 43, 66, 67, 73, 109, 113–115, 117–119, 175, 184, 187, 189, 200, 208, 234, 241, 267, 276, 287, 291, 293, 326, 328, 330, 332, 334 Auslander-Buchsbaum formula, 123, 124, 284, 310, 334, 336 Auslander-Reiten quiver, 217, 225, 224–240, 269, 276–283, 290, 293, 298 Auslander-Reiten sequence, 114, 160, 217, 217–232, 234, 238, 239, 267, 277, 281, 287–293, 295 existence, 218 uniqueness, 218 Auslander-Reiten translate τ, 222, 222–232, 235–237, 281, 289, 292, 296 Azumaya, Gorˆ o, 1, 3, 5 Baeth, Nicholas, 56 Bass numbers, 183, 201 Bass’ Conjecture, 176 Bass, Hyman, 48, 54, 57, 176 BD, see Burban-Drozd Betti numbers, 151, 184, 280, 298 biduality, 205, 264 binary polyhedral group, 84, 86, 86–90, 92–97, 151, 263 biproduct, 1, 2, 10, 32 blowup, 102, 103 bounded CM type, 30, 150, 163, 268, 268, 276, 279, 280, 297–307 bounded free resolution, 126 bounded representation type, 30, 267 Bourbaki, 23, 84, 170 Bourbaki sequence, 24, 24 branch locus, 326, 336 branch of a curve, 19, 146–149 Brauer, Richard, 267 Brauer-Thrall Conjectures, 267–280, 285 I, 268, 276–287 II, 49, 268, 280–285 Braun, Amiram, 334 Bravais, Auguste, 84 Bruns, Winfried, 284 Bruns-Herzog, 310 Buchsbaum, David, 66, 326, 328 Buchweitz, Ragnar-Olaf, 141, 145, 175, 184, 187, 189, 203, 208, 241, 245, 252, 284 Burban, Igor, 241, 244, 245, 248, 263 Burban-Drozd triples BD, 248, 244–259, 264–266 C, 86 c, 42 cancellative semigroup, 14 canonical module ω, 116, 176, 175–181, 183–185, 187–189, 193, 194, 196–202, 217, 218, 221–224, 228, 233, 234, 243, 263, 264, 281, 287, 288, 292, 313 canonical rank ω-rank, 190, 193, 195, 201 Cartan invariants, 267
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