366 INDEX special orthogonal group SO(3), 84, 85 special unitary group SU(n), 84, 85 spectral sequence, 221 splitting number spl(R), 22, 23 square root of −1, 86, 133, 137, 154, 253 stable Hom module Hom, 203–207, 216 category, 139 endomorphism ring End, 203, 207, 222, 223, 290 equivalence, 204 MCM trace, 201 module, 126, 129, 131, 132, 136, 137, 150, 190, 192, 194, 195, 284 stable ideal, 44, 56 Steinitz, Ernst, 10 Steinke, unther, 159, 160 stereographic projection, 85 stretched ring, 294, 295 strict transform, 104 strictly positive vector, 21, 25 striped matrix, 29 Striuli, Janet, 110, 111, 203, 210 strongly unbounded representation type, 267, 283 Strooker, Jan R., 182 stubbornness, 175 sub-additive function, 91, 102 subsemigroup expanded, 14, 16, 22, 23 full, 14, 16, 25, 26 surface singularity, 98–101, 104, 119, 245 Swan, Richard G., 3 system of parameters, faithful, 271, 271–280, 285 syzygy, 112, 113, 116, 126, 128, 134, 136–138, 150, 166, 185, 189, 194, 196, 197, 200, 205, 206, 219, 220, 242, 280, 284, 289, 309, 311, 312, 313 infinite, 209 reduced, see reduced sygyzy Szpiro, Lucien, 176 T , 86 Takahashi, Ryo, 203, 210 Tangent Lemma, 147 tangent line of an analytic curve, 146–149 Tate, John, 151 τ, 222 tedium, 172 tetrahedron, 84 Thrall, Robert M., 267 Threlfall, William, 86 topology, 117 torsion, 309 torsion module, 178, 189, 250, 252, 309, 329 torsion submodule, 41, 166, 246, 247, 310 torsion-free module, 14, 20, 21, 24, 41, 42, 52, 55–58, 69, 166, 178, 206, 247, 250, 251, 264, 307, 309, 327, 330, 331 torsionless module, 205, 206 total quotient ring, 17, 41, 42, 44, 45, 52, 59, 60, 177, 245, 246, 248, 249, 254, 306, 309, 316 totally acyclic complex, 209 totally reflexive module, 203, 209, 209–215 Tr, 204 trace, 63, 93, 328 trace ideal, 198, 198, 199, 201 trivial matrix factorization, 124, 125, 132 trivial module, 65, 73 trivial representation, 73, 74, 104, 292 truncated diagonal, 28 twisted group ring, see skew group ring type, 116, 193 ubiquity, 54, 83 Ulrich, Bernd, 313 unbounded CM type, 31, 297, 301 unbounded representation type, 267 uncountable CM type, 263, 268, 280, 284, 285 uncountable field, 142, 144, 241, 242, 284, 285 unique factorization, 3, 300, 317
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