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Finite algebra

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Being a finite algebra is a stronger condition than being an
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may be too technical for most readers to understand
681: 661: 600: 577: 548: 519: 477: 420: 400: 365: 330: 268: 248: 224: 204: 165: 141: 113: 90: 916: 717: 899: 842: 366:{\displaystyle W\subseteq \mathbb {A} ^{m}} 331:{\displaystyle V\subseteq \mathbb {A} ^{n}} 291:This concept is closely related to that of 906: 892: 849: 835: 676: 415: 353: 318: 59:Learn how and when to remove this message 43:, without removing the technical details. 520:{\displaystyle \phi ^{*}f=f\circ \phi } 917: 751: 287:Finite morphisms in algebraic geometry 41:make it understandable to non-experts 858: 801: 15: 728:Introduction to commutative algebra 610:finite morphism of affine varieties 13: 755:Algebraic Geometry An Introduction 647: 632: 563: 534: 463: 448: 401:{\displaystyle \phi \colon V\to W} 14: 956: 862: 805: 20: 697:can be found in the article on 745: 711: 656: 650: 644: 641: 635: 572: 566: 543: 537: 472: 466: 460: 457: 451: 408:, the induced homomorphism of 392: 205:{\displaystyle f\colon R\to A} 196: 1: 704: 303:, given two affine varieties 173:-algebra can be thought as a 878:. You can help Knowledge by 821:. You can help Knowledge by 7: 776: 10: 961: 857: 800: 788:Finitely generated algebra 578:{\displaystyle \Gamma (W)} 549:{\displaystyle \Gamma (V)} 299:; in the simplest case of 945:Commutative algebra stubs 793:Finitely generated module 731:. CRC Press. p. 30. 940:Algebraic geometry stubs 758:. Springer. p. 82. 669:is a finite morphism of 752:Perrin, Daniel (2008). 719:Atiyah, Michael Francis 874:-related article is a 817:–related article is a 693:The generalisation to 683: 682:{\displaystyle \Bbbk } 663: 602: 579: 550: 521: 479: 422: 421:{\displaystyle \Bbbk } 402: 367: 332: 281:algebra of finite type 270: 250: 226: 206: 167: 143: 115: 92: 684: 664: 603: 601:{\displaystyle \phi } 580: 551: 522: 480: 423: 403: 368: 333: 271: 251: 227: 207: 168: 144: 116: 93: 723:Macdonald, Ian Grant 673: 616: 592: 560: 531: 489: 432: 412: 380: 375:dominant regular map 342: 307: 260: 240: 216: 184: 157: 133: 105: 82: 925:Commutative algebra 872:commutative algebra 77:associative algebra 930:Algebraic geometry 815:algebraic geometry 679: 659: 598: 575: 546: 517: 475: 418: 398: 363: 328: 297:algebraic geometry 266: 246: 222: 202: 163: 139: 127:finitely generated 111: 88: 887: 886: 830: 829: 765:978-1-84800-056-8 269:{\displaystyle R} 249:{\displaystyle A} 225:{\displaystyle f} 166:{\displaystyle R} 142:{\displaystyle R} 114:{\displaystyle R} 91:{\displaystyle A} 69: 68: 61: 952: 908: 901: 894: 866: 859: 851: 844: 837: 809: 802: 770: 769: 749: 743: 742: 715: 699:finite morphisms 688: 686: 685: 680: 668: 666: 665: 660: 628: 627: 607: 605: 604: 599: 584: 582: 581: 576: 555: 553: 552: 547: 526: 524: 523: 518: 501: 500: 484: 482: 481: 476: 444: 443: 427: 425: 424: 419: 407: 405: 404: 399: 372: 370: 369: 364: 362: 361: 356: 337: 335: 334: 329: 327: 326: 321: 301:affine varieties 275: 273: 272: 267: 255: 253: 252: 247: 231: 229: 228: 223: 211: 209: 208: 203: 172: 170: 169: 164: 148: 146: 145: 140: 120: 118: 117: 112: 97: 95: 94: 89: 73:abstract algebra 64: 57: 53: 50: 44: 24: 23: 16: 960: 959: 955: 954: 953: 951: 950: 949: 915: 914: 913: 912: 856: 855: 798: 783:Finite morphism 779: 774: 773: 766: 750: 746: 739: 716: 712: 707: 674: 671: 670: 623: 619: 617: 614: 613: 593: 590: 589: 561: 558: 557: 532: 529: 528: 496: 492: 490: 487: 486: 439: 435: 433: 430: 429: 413: 410: 409: 381: 378: 377: 357: 352: 351: 343: 340: 339: 322: 317: 316: 308: 305: 304: 293:finite morphism 289: 261: 258: 257: 241: 238: 237: 234:finite morphism 217: 214: 213: 212:, in this case 185: 182: 181: 158: 155: 154: 134: 131: 130: 106: 103: 102: 83: 80: 79: 65: 54: 48: 45: 37:help improve it 34: 25: 21: 12: 11: 5: 958: 948: 947: 942: 937: 932: 927: 911: 910: 903: 896: 888: 885: 884: 867: 854: 853: 846: 839: 831: 828: 827: 810: 796: 795: 790: 785: 778: 775: 772: 771: 764: 744: 737: 709: 708: 706: 703: 691: 690: 678: 658: 655: 652: 649: 646: 643: 640: 637: 634: 631: 626: 622: 597: 574: 571: 568: 565: 545: 542: 539: 536: 516: 513: 510: 507: 504: 499: 495: 474: 471: 468: 465: 462: 459: 456: 453: 450: 447: 442: 438: 417: 397: 394: 391: 388: 385: 360: 355: 350: 347: 325: 320: 315: 312: 288: 285: 265: 245: 221: 201: 198: 195: 192: 189: 162: 138: 110: 87: 67: 66: 28: 26: 19: 9: 6: 4: 3: 2: 957: 946: 943: 941: 938: 936: 933: 931: 928: 926: 923: 922: 920: 909: 904: 902: 897: 895: 890: 889: 883: 881: 877: 873: 868: 865: 861: 860: 852: 847: 845: 840: 838: 833: 832: 826: 824: 820: 816: 811: 808: 804: 803: 799: 794: 791: 789: 786: 784: 781: 780: 767: 761: 757: 756: 748: 740: 738:9780201407518 734: 730: 729: 724: 720: 714: 710: 702: 700: 696: 653: 638: 629: 624: 620: 611: 595: 588: 587: 586: 569: 540: 514: 511: 508: 505: 502: 497: 493: 469: 454: 445: 440: 436: 395: 389: 386: 383: 376: 358: 348: 345: 323: 313: 310: 302: 298: 294: 284: 282: 277: 263: 243: 235: 219: 199: 193: 190: 187: 180: 176: 160: 152: 136: 128: 124: 108: 101: 85: 78: 74: 63: 60: 52: 42: 38: 32: 29:This article 27: 18: 17: 880:expanding it 869: 823:expanding it 812: 797: 754: 747: 727: 713: 692: 609: 290: 278: 256:is a finite 233: 232:is called a 175:homomorphism 122: 70: 55: 49:January 2020 46: 30: 585:-algebra: 485:defined by 919:Categories 705:References 689:-algebras. 428:-algebras 276:-algebra. 121:is called 677:k 648:Γ 645:→ 633:Γ 630:: 625:∗ 621:ϕ 596:ϕ 564:Γ 535:Γ 515:ϕ 512:∘ 498:∗ 494:ϕ 464:Γ 461:→ 449:Γ 446:: 441:∗ 437:ϕ 416:k 393:→ 387:: 384:ϕ 349:⊆ 314:⊆ 197:→ 191:: 125:if it is 935:Algebras 777:See also 725:(1994). 695:schemes 556:into a 98:over a 35:Please 762:  735:  527:turns 373:and a 151:module 129:as an 123:finite 870:This 813:This 608:is a 179:rings 153:. An 75:, an 876:stub 819:stub 760:ISBN 733:ISBN 100:ring 612:if 295:in 236:if 177:of 71:In 39:to 921:: 721:; 701:. 338:, 283:. 907:e 900:t 893:v 882:. 850:e 843:t 836:v 825:. 768:. 741:. 657:) 654:V 651:( 642:) 639:W 636:( 573:) 570:W 567:( 544:) 541:V 538:( 509:f 506:= 503:f 473:) 470:V 467:( 458:) 455:W 452:( 396:W 390:V 359:m 354:A 346:W 324:n 319:A 311:V 264:R 244:A 220:f 200:A 194:R 188:f 161:R 149:- 137:R 109:R 86:A 62:) 56:( 51:) 47:( 33:.

Index

help improve it
make it understandable to non-experts
Learn how and when to remove this message
abstract algebra
associative algebra
ring
finitely generated
module
homomorphism
rings
algebra of finite type
finite morphism
algebraic geometry
affine varieties
dominant regular map
schemes
finite morphisms
Atiyah, Michael Francis
Macdonald, Ian Grant
Introduction to commutative algebra
ISBN
9780201407518
Algebraic Geometry An Introduction
ISBN
978-1-84800-056-8
Finite morphism
Finitely generated algebra
Finitely generated module
Stub icon
algebraic geometry

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