INDEX 363 minimal MCM approximation, 180, 180, 182–184, 186, 188–192, 196, 200, 201, 228, 231, 234, 278, 282 uniqueness, 182 minimal multiplicity, 101, 106, 120, 151, 202, 294, 295 minimal polynomial, 30, 38 minimal prime ideal, 13, 17, 19, 20, 39, 45, 56, 58, 60, 127, 170, 177, 178, 305, 306, 310, 312, 316, 318 minimal reduction, 44, 101, 171, 301, 314 minimal resolution of singularities, 98–101, 104 Miyata’s Theorem, 109, 112–114, 197 Miyata, Takehiko, 109 modified Burban-Drozd triples BD , see Burban-Drozd triples BD module canonical, 116, 175, 180, 181, 183–185, 187–189, 193, 194, 196–202, 217, 218, 221–224, 228, 233, 234, 243, 263, 264, 281, 287, 288, 292, 313 conormal I/I2, 116 extended, 17, 18, 23, 24, 26, 43, 164, 169, 305, 306 faithful, 305 Gorenstein, 179, 313 maximal Cohen-Macaulay, 29 MCM, 29 n-torsionless, 205, 206 of covariants, 72, 152 of finite length, 10, 17, 18, 24, 45, 49, 55, 60, 99, 106, 110, 112, 114, 115, 120, 121, 175, 183, 184, 206, 221, 222, 246, 247, 264, 267–270, 276, 278, 279, 296, 310, 313, 316, 332, 334, 336 projective, 20, 32, 43, 44, 46, 47, 56, 61, 64, 65, 70–73, 78, 83, 177, 230, 238, 249, 250, 306, 311, 323, 325, 328–330 reflexive, 14, 24, 25, 81, 82, 82, 83, 104, 106, 119, 150, 205, 206, 220, 221, 246, 250, 252, 264, 311–313, 327, 329–334, 336 simple, 73, 270 stable, 126, 129, 131, 132, 136, 137, 150, 190, 192, 194, 195, 284 torsion, 178, 189, 250, 252, 329 torsion-free, 14, 20, 21, 24, 41, 42, 52, 55–58, 69, 166, 178, 206, 247, 250, 251, 264, 307, 309, 327, 330, 331 torsionless, 205, 206 totally reflexive, 209, 209–215 trivial, 65, 73 Ulrich, 315 weakly extended, 43, 47, 59, 165–167, 171 weakly liftable, 43 monoid, see semigroup μR(M), 315 multiplicity, 41, 44, 54–56, 100, 101, 106, 116, 160, 267, 276, 280–283, 294, 297, 299, 301, 302, 307, 313, 314–316 multiplicity two, 42, 54, 57, 60, 101, 106, 142, 143, 145, 146, 268, 295, 298, 299, 303, 304 Mumford, David, 100, 117–119 n-torsionless module, 205, 206 Nagata, Masayoshi, 275 NAK, see Nakayama’s Lemma Nakayama’s Lemma, 6, 9, 20, 31, 44, 47, 72, 181, 215, 272, 279, 282, 318, 321, 333 Nazarova, Liudmila A., 267 nc-local, 3, 5, 10 endomorphism ring, 1, 3–6, 10, 134, 203, 218, 223, 225, 226, 238, 272, 273 negative definite matrix, 100, 102, 117 nilpotent Jordan block, 29 nilpotent Jordan block, 28, 31, 34, 37 nilradical, 53, 54, 301, 302, 305 nodal cubic curve, 46, 58, 148 Noether, Emmy, 77, 328 non-constant ranks, 57 non-derogatory matrix, 30 non-free locus, 284 non-normal locus, 246 non-singular ring, 116 norm, 78
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