INDEX 365 reflection, 79, 151, 153, 335 reflection group, 155 reflexive module, 14, 24, 25, 81, 82, 82, 83, 104, 106, 119, 150, 205–207, 220, 221, 246, 250, 252, 264, 311–313, 327, 329–334, 336 reflexive product, 106, 234, 246, 264, 327 reflexive subcategory, 211, 212, 215 regular homomorphism, 167, 169, 170 regular in codimension one, 245, 246, 311 regular local ring, 53, 69, 78, 106, 115, 116, 118, 119, 123, 124, 128, 149, 151, 160, 169, 194, 195, 200, 242, 243, 246, 249, 257, 273–275, 285, 311, 315, 330, 333, 334, 336 Reiner, Irving, 31, 38, 41, 45, 49, 50 Reiten, Idun, 91, 177, 287, 291, 293 Remak, Robert E., 1 representation theory of Artin algebras, 217 of finite groups, 61, 71, 72, 81, 97, 151 of finite-dimensional algebras, 267 of lattices over orders, 50 resolution of singularities, 97–104 retraction, 77 Reynolds operator, 62, 63, 65, 90 Riemann-Roch Theorem, 101 right minimal homomorphism, 180, 211–213, 226 right minimal MCM approximation, 180, 180, 182, 183 Roberts, Paul C., 176 Roczen, Marko, 280 Ro˘ ıter, Andre˘ ı V., 32, 38, 50, 267 S#G, 64 (S1), 66, 67, 310 (S2), 66, 67, 82, 245, 264, 266, 311, 312, 326, 329 Saito, Kyoji, 192 Sally, Judith D., 44 Sanders, Herbert, 298 Schanuel’s Lemma, 166, 180, 311 Schmidt, Otto, 1 Schreyer, Frank-Olaf, 141, 145, 163, 241, 245, 252, 260, 262, 263, 284 Schur’s Lemma, 93 scroll, 291, 291, 294, 295 self-intersection, 100, 101 semigroup, 13, 14 cancellative, 14 finitely generated, 13 reduced, 14 seminormal, 49, 50, 59 seminormalization, 49 separable algebra, 324, 325 separable field extension, 36, 38, 49–51, 66, 117, 163, 164, 170–172, 321, 324–330, 339 series of singularities, 260, 262 Serre’s conditions (S1), 66, 67, 310 (S2), 66, 67, 82, 245, 264, 266, 311, 312, 326, 329 (Sn), 309, 310, 311, 312, 325 Serre’s criterion for normality, 245, 295, 311, 325 Sharp, Rodney, 177 sharping, 128, 130, 133, 137 sheafification, 106 shenanigans, 137 Shida, Akira, 180, 182 Simon, Anne-Marie, 182 simple module, 73, 270 simple singularity, 51, 141, 142, 143, 145, 146, 149, 160, 173, 253, 259, 297 singular locus, 167, 241, 242, 263, 275, 284 skew group ring S#G, 61, 64, 65, 67, 69–74, 78, 83, 135, 230, 292, 330, 336 Smalø, Sverre, 268, 280–283 small subgroup, 69, 72, 339 (Sn), 310 Snake Lemma, 109, 188, 218, 226, 247, 251, 252 socle, 101, 201, 223 Solberg, Øyvind, 43, 160 special linear group SL(n, k), 81, 83, 84, 86, 90, 92, 93, 104, 151, 152, 229
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