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Monomial conjecture

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378: 22: 307: 419: 325: 198: 32: 412: 448: 405: 90: 62: 47: 69: 438: 76: 58: 377: 443: 385: 313: 112: 83: 389: 138: 131: 120: 345: 432: 302:{\displaystyle x_{1}^{t}\cdots x_{d}^{t}\not \in (x_{1}^{t+1},\dots ,x_{d}^{t+1}).\,} 185: 39: 21: 134: 346:"Local Cohomology and the Homological Conjectures in Commutative Algebra" 15: 393: 43: 201: 301: 312:The statement can relatively easily be shown in 326:Homological conjectures in commutative algebra 413: 8: 48:introducing citations to additional sources 420: 406: 298: 280: 275: 250: 245: 229: 224: 211: 206: 200: 38:Relevant discussion may be found on the 337: 188:). Then for all positive integers  7: 374: 372: 392:. You can help Knowledge (XXG) by 14: 376: 31:relies largely or entirely on a 20: 292: 238: 160:be a system of parameters for 115:, a field of mathematics, the 1: 465: 371: 449:Commutative algebra stubs 388:-related article is a 303: 304: 59:"Monomial conjecture" 199: 123:says the following: 44:improve this article 439:Commutative algebra 386:commutative algebra 353:www5a.biglobe.ne.jp 314:characteristic zero 291: 261: 234: 216: 117:monomial conjecture 113:commutative algebra 299: 271: 241: 220: 202: 401: 400: 175:, ...,  151:, ...,  109: 108: 94: 456: 422: 415: 408: 380: 373: 363: 362: 360: 359: 350: 342: 308: 306: 305: 300: 290: 279: 260: 249: 233: 228: 215: 210: 104: 101: 95: 93: 52: 24: 16: 464: 463: 459: 458: 457: 455: 454: 453: 429: 428: 427: 426: 369: 367: 366: 357: 355: 348: 344: 343: 339: 334: 322: 197: 196: 183: 174: 159: 150: 139:Krull dimension 121:Melvin Hochster 105: 99: 96: 53: 51: 37: 25: 12: 11: 5: 462: 460: 452: 451: 446: 441: 431: 430: 425: 424: 417: 410: 402: 399: 398: 381: 365: 364: 336: 335: 333: 330: 329: 328: 321: 318: 310: 309: 297: 294: 289: 286: 283: 278: 274: 270: 267: 264: 259: 256: 253: 248: 244: 240: 237: 232: 227: 223: 219: 214: 209: 205: 179: 172: 155: 148: 107: 106: 42:. Please help 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 461: 450: 447: 445: 442: 440: 437: 436: 434: 423: 418: 416: 411: 409: 404: 403: 397: 395: 391: 387: 382: 379: 375: 370: 354: 347: 341: 338: 331: 327: 324: 323: 319: 317: 315: 295: 287: 284: 281: 276: 272: 268: 265: 262: 257: 254: 251: 246: 242: 235: 230: 225: 221: 217: 212: 207: 203: 195: 194: 193: 191: 187: 186:Artinian ring 182: 178: 171: 167: 163: 158: 154: 147: 143: 140: 136: 133: 129: 124: 122: 118: 114: 103: 92: 89: 85: 82: 78: 75: 71: 68: 64: 61: –  60: 56: 55:Find sources: 49: 45: 41: 35: 34: 33:single source 29:This article 27: 23: 18: 17: 394:expanding it 383: 368: 356:. Retrieved 352: 340: 311: 189: 180: 176: 169: 165: 161: 156: 152: 145: 141: 127: 125: 116: 110: 97: 87: 80: 73: 66: 54: 30: 444:Conjectures 433:Categories 358:2023-12-19 332:References 192:, we have 135:local ring 132:Noetherian 70:newspapers 266:… 218:⋯ 164:(so that 40:talk page 320:See also 236:∉ 184:) is an 144:and let 100:May 2024 84:scholar 86:  79:  72:  65:  57:  384:This 349:(PDF) 130:be a 91:JSTOR 77:books 390:stub 126:Let 63:news 137:of 119:of 111:In 46:by 435:: 351:. 316:. 168:/( 421:e 414:t 407:v 396:. 361:. 296:. 293:) 288:1 285:+ 282:t 277:d 273:x 269:, 263:, 258:1 255:+ 252:t 247:1 243:x 239:( 231:t 226:d 222:x 213:t 208:1 204:x 190:t 181:d 177:x 173:1 170:x 166:A 162:A 157:d 153:x 149:1 146:x 142:d 128:A 102:) 98:( 88:· 81:· 74:· 67:· 50:. 36:.

Index


single source
talk page
improve this article
introducing citations to additional sources
"Monomial conjecture"
news
newspapers
books
scholar
JSTOR
commutative algebra
Melvin Hochster
Noetherian
local ring
Krull dimension
Artinian ring
characteristic zero
Homological conjectures in commutative algebra
"Local Cohomology and the Homological Conjectures in Commutative Algebra"
Stub icon
commutative algebra
stub
expanding it
v
t
e
Categories
Commutative algebra
Conjectures

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