INDEX 359 extension of modules, 109–111, 115, 120, 127, 179, 187, 223, 290, 291 exterior power p , 65, 73, 74, 231, 292 faithful flatness, 17, 18, 26, 27, 163, 314 faithful ideal, 53, 55, 56, 283 faithful module, 305 faithful system of parameters, 271, 271–280, 285 faithfully flat descent, 15, 24, 25, 215 Ferrand, Daniel, 178 fiber product, 323 FID hull, see hull of finite injective dimension field algebraically closed, 51, 73, 90, 92, 98, 101, 118, 128, 133, 134, 137, 138, 141, 142, 144–147, 151, 159, 160, 163, 172, 192, 225, 234, 253, 259, 262, 268, 276, 277, 279–283, 285, 287, 288, 293, 299, 321, 323 characteristic p, see characteristic characteristic zero, 109, 116 coefficient, 299 finite, 38 imperfect, 275 infinite, 33, 34, 39, 43, 44, 49–51, 142, 144, 171, 195, 202, 267, 268, 281, 285, 291, 297, 301, 302, 304, 314 perfect, 52, 141, 267, 268, 275, 276, 279 uncountable, 142, 144, 241, 242, 284, 285 field extension algebraic, 167, 174 Galois, 63, 117–119, 330, 335, 337 inseparable, 36, 49, 163, 172 non-Galois, 38 separable, 36, 38, 49–51, 66, 117, 163, 164, 170–172, 321, 324–330, 339 finite birational extension, 42, 43, 44, 49, 51, 52, 172, 237, 295, 300–303, 307, 316, 317 finite CM type, 29, 41, 45, 46, 48–54, 56, 57, 75, 81–83, 91, 115, 117–120, 132, 133, 141, 145, 146, 149–151, 159, 160, 163–166, 168–174, 199, 203, 210, 237, 243, 245, 268, 276, 279, 285, 287–296, 299, 304, 306 =⇒ isolated singularity, 109, 113, 115, 165, 169, 199, 276 ascent of, 53, 54 finite field, 38 finite injective dimension, 175, 176, 178, 193, 201, 221 finite length module, 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 finite representation type, 29, 30, 32, 38, 47, 49, 116, 212, 267 of Artinian pairs, 29, 32, 46 TR modules, 209 finite TR type, 209, 210 finite-dimensional algebra, 33, 267, 268, 317, 318 Fitting’s Lemma, 10, 269 Five Lemma, 261 flatness, 164, 321 flatting, 128, 130, 133, 137, 234, 237 Flenner, Hubert, 98, 117, 118 formally equidimensional, 170 Foxby, Hans-Bjørn, 177 fractional ideal, 10, 24, 292, 296, 328 fractional linear transformations, 85 free monoid, 13, 16 free rank f-rank, 189, 191, 192, 194–196, 199 free resolution, 206–208 bounded, 126, 151 periodic, 126 free semigroup, 22 full subsemigroup, 14, 16, 25, 26 fundamental divisor Zf , 100–102, 104 fundamental group π1, 117 fundamental sequence, 233, 234
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