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System of parameters

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Every local Noetherian ring admits a system of parameters.
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that satisfies any of the following equivalent conditions:
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Mathematical concept in dimension theory of local rings
49:. Unsourced material may be challenged and removed. 280:elements to generate an ideal whose radical is 470: 8: 303:-dimensional module over a local ring, then 410:. University of Michigan. September 5, 2007 477: 463: 109:Learn how and when to remove this message 405:"Math 711: Lecture of September 5, 2007" 396: 7: 431: 429: 47:adding citations to reliable sources 376:Introduction to commutative algebra 276:It is not possible for fewer than 14: 433: 23: 34:needs additional citations for 284:because then the dimension of 1: 449:. You can help Knowledge by 522: 428: 506:Commutative algebra stubs 368:Atiyah, Michael Francis 445:-related article is a 58:"System of parameters" 150:is a set of elements 501:Ideals (ring theory) 321:system of parameters 127:system of parameters 43:improve this article 496:Commutative algebra 443:commutative algebra 288:would be less than 361:General references 458: 457: 227:is contained in ( 119: 118: 111: 93: 513: 479: 472: 465: 437: 430: 420: 419: 417: 415: 409: 401: 386: 372:Macdonald, I. G. 356: 114: 107: 103: 100: 94: 92: 51: 27: 19: 521: 520: 516: 515: 514: 512: 511: 510: 486: 485: 484: 483: 426: 424: 423: 413: 411: 407: 403: 402: 398: 393: 366: 363: 351: 342: 332: 318: 309: 261: 252: 242: 233: 215: 206: 192: 183: 165: 156: 138:Krull dimension 134:Noetherian ring 115: 104: 98: 95: 52: 50: 40: 28: 17: 12: 11: 5: 519: 517: 509: 508: 503: 498: 488: 487: 482: 481: 474: 467: 459: 456: 455: 438: 422: 421: 395: 394: 392: 389: 388: 387: 362: 359: 347: 340: 314: 307: 271: 270: 257: 250: 244: 238: 231: 223:Some power of 221: 211: 204: 194: 188: 181: 161: 154: 117: 116: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 518: 507: 504: 502: 499: 497: 494: 493: 491: 480: 475: 473: 468: 466: 461: 460: 454: 452: 448: 444: 439: 436: 432: 427: 406: 400: 397: 390: 385: 381: 377: 373: 369: 365: 364: 360: 358: 355: 350: 346: 339: 335: 330: 326: 322: 317: 313: 306: 302: 298: 293: 291: 287: 283: 279: 274: 268: 266: 260: 256: 249: 245: 241: 237: 230: 226: 222: 219: 214: 210: 203: 199: 195: 191: 187: 180: 176: 175:minimal prime 172: 169: 168: 167: 164: 160: 153: 149: 146: 145:maximal ideal 142: 139: 135: 132: 128: 124: 113: 110: 102: 91: 88: 84: 81: 77: 74: 70: 67: 63: 60: –  59: 55: 54:Find sources: 48: 44: 38: 37: 32:This article 30: 26: 21: 20: 451:expanding it 440: 425: 412:. Retrieved 399: 375: 353: 348: 344: 337: 333: 324: 320: 315: 311: 304: 300: 296: 294: 289: 285: 281: 277: 275: 272: 264: 258: 254: 247: 239: 235: 228: 224: 217: 212: 208: 201: 189: 185: 178: 170: 162: 158: 151: 147: 140: 126: 120: 105: 96: 86: 79: 72: 65: 53: 41:Please help 36:verification 33: 357:is finite. 123:mathematics 490:Categories 391:References 69:newspapers 374:(1969), 267:-primary 99:May 2022 414:May 31, 384:0242802 343:, ..., 327:if the 310:, ..., 253:, ..., 234:, ..., 207:, ..., 198:radical 184:, ..., 157:, ..., 83:scholar 382:  329:length 177:over ( 129:for a 85:  78:  71:  64:  56:  441:This 408:(PDF) 319:is a 299:is a 262:) is 216:) is 173:is a 143:with 131:local 90:JSTOR 76:books 447:stub 416:2022 323:for 200:of ( 196:The 125:, a 62:news 336:/ ( 331:of 295:If 136:of 121:In 45:by 492:: 380:MR 370:; 352:) 292:. 243:). 193:). 478:e 471:t 464:v 453:. 418:. 354:M 349:k 345:x 341:1 338:x 334:M 325:M 316:k 312:x 308:1 305:x 301:k 297:M 290:d 286:R 282:m 278:d 269:. 265:m 259:d 255:x 251:1 248:x 246:( 240:d 236:x 232:1 229:x 225:m 220:. 218:m 213:d 209:x 205:1 202:x 190:d 186:x 182:1 179:x 171:m 163:d 159:x 155:1 152:x 148:m 141:d 112:) 106:( 101:) 97:( 87:· 80:· 73:· 66:· 39:.

Index


verification
improve this article
adding citations to reliable sources
"System of parameters"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
mathematics
local
Noetherian ring
Krull dimension
maximal ideal
minimal prime
radical
m-primary
length
Atiyah, Michael Francis
Macdonald, I. G.
MR
0242802
"Math 711: Lecture of September 5, 2007"
Stub icon
commutative algebra
stub
expanding it
v

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