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Hilbert–Burch theorem

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481: 175: 261: 95: 522: 66:, p. 944) proved a more general version. Several other authors later rediscovered and published variations of this theorem. 515: 551: 508: 406: 361: 233: 394: 349: 170:{\displaystyle 0\rightarrow R^{m}{\stackrel {f}{\rightarrow }}R^{n}\rightarrow R\rightarrow R/I\rightarrow 0} 546: 541: 496: 428: 371: 318: 185: 47: 28: 457: 416: 379: 334: 8: 488: 83: 16:
Describes the structure of some free resolutions of a quotient of a local or graded ring
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The Geometry of Syzygies. A second course in commutative algebra and algebraic geometry
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Burch, Lindsay (1968), "On ideals of finite homological dimension in local rings",
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Commutative algebra. With a view toward algebraic geometry
426:(1890), "Ueber die Theorie der algebraischen Formen", 236: 98: 255: 169: 533: 70:, theorem 20.15) gives a statement and proof. 516: 523: 509: 256:{\displaystyle \operatorname {Fitt} _{1}I} 385: 340: 67: 422: 58:) proved a version of this theorem for 55: 534: 288: 63: 475: 352:, vol. 150, Berlin, New York: 267:, i.e., the ideal generated by the 13: 46:in the case that the quotient has 14: 563: 479: 227:, a depth-2 ideal, is the first 27:describes the structure of some 397:, vol. 229, New York, NY: 161: 147: 141: 119: 102: 1: 395:Graduate Texts in Mathematics 350:Graduate Texts in Mathematics 282: 203: – 1 and the ideal 495:. You can help Knowledge by 291:Proc. Cambridge Philos. Soc. 180:is a free resolution of the 73: 7: 10: 568: 474: 552:Commutative algebra stubs 303:10.1017/S0305004100043620 82:is a local ring with an 491:-related article is a 271:of the minors of size 257: 171: 429:Mathematische Annalen 258: 172: 25:Hilbert–Burch theorem 234: 96: 48:projective dimension 547:Theorems in algebra 542:Commutative algebra 489:commutative algebra 442:10.1007/BF01208503 253: 167: 62:, and Burch ( 504: 503: 275:of the matrix of 128: 559: 525: 518: 511: 483: 476: 468: 419: 382: 337: 262: 260: 259: 254: 246: 245: 176: 174: 173: 168: 157: 140: 139: 130: 129: 127: 122: 117: 114: 113: 60:polynomial rings 29:free resolutions 567: 566: 562: 561: 560: 558: 557: 556: 532: 531: 530: 529: 472: 409: 399:Springer-Verlag 387:Eisenbud, David 364: 354:Springer-Verlag 342:Eisenbud, David 285: 241: 237: 235: 232: 231: 153: 135: 131: 123: 118: 116: 115: 109: 105: 97: 94: 93: 76: 17: 12: 11: 5: 565: 555: 554: 549: 544: 528: 527: 520: 513: 505: 502: 501: 484: 470: 469: 436:(4): 473–534, 424:Hilbert, David 420: 407: 383: 362: 338: 297:(4): 941–948, 284: 281: 252: 249: 244: 240: 178: 177: 166: 163: 160: 156: 152: 149: 146: 143: 138: 134: 126: 121: 112: 108: 104: 101: 75: 72: 68:Eisenbud (1995 15: 9: 6: 4: 3: 2: 564: 553: 550: 548: 545: 543: 540: 539: 537: 526: 521: 519: 514: 512: 507: 506: 500: 498: 494: 490: 485: 482: 478: 477: 473: 467: 463: 459: 455: 451: 447: 443: 439: 435: 432:(in German), 431: 430: 425: 421: 418: 414: 410: 408:0-387-22215-4 404: 400: 396: 392: 388: 384: 381: 377: 373: 369: 365: 363:3-540-94268-8 359: 355: 351: 347: 343: 339: 336: 332: 328: 324: 320: 316: 312: 308: 304: 300: 296: 292: 287: 286: 280: 278: 274: 270: 266: 250: 247: 242: 238: 230: 229:Fitting ideal 226: 222: 218: 214: 210: 206: 202: 199: =  198: 194: 190: 187: 183: 164: 158: 154: 150: 144: 136: 132: 124: 110: 106: 99: 92: 91: 90: 88: 85: 81: 71: 69: 65: 61: 57: 53: 49: 45: 42: 38: 34: 30: 26: 22: 497:expanding it 486: 471: 433: 427: 390: 345: 294: 290: 276: 272: 269:determinants 264: 224: 220: 212: 208: 204: 200: 196: 192: 188: 181: 179: 86: 79: 77: 24: 18: 219:element of 21:mathematics 536:Categories 458:22.0133.01 417:1066.14001 380:0819.13001 335:0172.32302 283:References 466:179177713 450:0025-5831 327:123231429 311:0008-1981 248:⁡ 162:→ 148:→ 142:→ 120:→ 103:→ 74:Statement 50: 2. 389:(2005), 344:(1995), 33:quotient 372:1322960 319:0229634 217:regular 195:, then 54: ( 52:Hilbert 464:  456:  448:  415:  405:  378:  370:  360:  333:  325:  317:  309:  211:where 186:module 41:graded 23:, the 487:This 462:S2CID 323:S2CID 215:is a 89:and 84:ideal 37:local 35:of a 31:of a 493:stub 446:ISSN 403:ISBN 358:ISBN 307:ISSN 239:Fitt 223:and 64:1968 56:1890 44:ring 454:JFM 438:doi 413:Zbl 376:Zbl 331:Zbl 299:doi 263:of 207:is 78:If 39:or 19:In 538:: 460:, 452:, 444:, 434:36 411:, 401:, 393:, 374:, 368:MR 366:, 356:, 348:, 329:, 321:, 315:MR 313:, 305:, 295:64 293:, 279:. 209:aJ 524:e 517:t 510:v 499:. 440:: 301:: 277:f 273:m 265:I 251:I 243:1 225:J 221:R 213:a 205:I 201:n 197:m 193:I 191:/ 189:R 184:- 182:R 165:0 159:I 155:/ 151:R 145:R 137:n 133:R 125:f 111:m 107:R 100:0 87:I 80:R

Index

mathematics
free resolutions
quotient
local
graded
ring
projective dimension
Hilbert
1890
polynomial rings
1968
Eisenbud (1995
ideal
module
regular
Fitting ideal
determinants
doi
10.1017/S0305004100043620
ISSN
0008-1981
MR
0229634
S2CID
123231429
Zbl
0172.32302
Eisenbud, David
Graduate Texts in Mathematics
Springer-Verlag

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