Volume (1953) no. 123

Algèbre locale

Samuel, Pierre

Mémorial des sciences mathématiques, no. 123 (1953) , 80 p.

MR 54995 | Zbl 0053.01901 | 21 citations in Numdam

@book{MSM_1953__123__1_0,
     author = {Samuel, Pierre},
     title = {Alg\`ebre locale},
     series = {M\'emorial des sciences math\'ematiques},
     publisher = {Gauthier-Villars},
     number = {123},
     year = {1953},
     zbl = {0053.01901},
     mrnumber = {54995},
     language = {fr},
     url = {http://www.numdam.org/item/MSM_1953__123__1_0}
}

Samuel, Pierre. Algèbre locale. Mémorial des sciences mathématiques, no. 123 (1953), 80 p. http://www.numdam.org/item/MSM_1953__123__1_0/

References

1. Abellanas. _ On the geometrical theory of algebraic surfaces for a perfect coefficient field of characteristic p (Rev. Acad. Ci. Madrid, t. 36, 1942, p. 482-499). | JFM 68.0063.01 | MR 23557 | Zbl 0028.08003

2. Ancochea. _ Courbes algébriques sur corps fermés de caractéristique quelconque (Acla Salmanticensia, t. 1, 1946). | MR 16912 | Zbl 0063.00081

3. Apery. _ Sur les branches superlinéaires des courbes algébriques (C. R. Acad. Sc., t. 222, 1946, p. 1198-1200). | MR 17942 | Zbl 0061.35404

4. Barsotti. _ Algebraic correspondences between algebraic varieties (Ann. of Math., t. 52, 1950, p. 427-464). | MR 37022 | Zbl 0041.28502

5. Bourbaki. _ Algèbre, Chap. I (Paris, Hermann, 1942, n° 934). | Zbl 0060.06808

6. Bourbaki. _ Algèbre, Chap. II (Paris, Hermann, 1947, n° 1032). | MR 23803

7. Bourbaki. _ Algèbre, Chap. III (Paris, Hermann, 1948, n° 1044). | MR 26989

8. Bourbaki. _ Algèbre, Chap. IV et V (Paris, Herman, 1950, n° 1102). | MR 35759

9. Bourbaki. _ Topologie générale, Chap. I et II (Paris, Herman, 1940, n° 858).

10. Bourbaki. _ Topologie générale, Chap. III et IV (Paris, Hermann, 1942, n° 916). | JFM 68.0507.01

11. Bourbaki. _ Topologie générale, Chap. IX (Paris, Hermann, 1948, n° 1045). | Zbl 0031.05502

12. H. Cartan. _ Sur l'homologie des espaces où opère un groupe (C. R. Acad. Sc., t. 226, 1948, p. 148-150). | MR 23523 | Zbl 0034.25603

13. Chevalley. _ On the theory of local rings (Ann. of Math., t. 44, 1943, p. 690-708). | MR 9603 | Zbl 0060.06908

14. Chevalley. _ On the notion of the ring of quotients of a prime ideal (Bull. Amer. Math. Soc., t. 50, 1944, p. 93-97). | MR 9946 | Zbl 0060.06907

15. Chevalley. _ Some properties of ideals in rings of power series (Trans. Amer. Math. Soc., t. 55, 1944, p. 68-84). | MR 10548 | Zbl 0060.06909

16. Chevalley. _ Intersections of algebraic and algebroid varieties (Trans. Amer. Math. Soc., t. 57, 1945, p. r-85). | MR 12458 | Zbl 0063.00841

17. Chow. _ On compact complex analytic varieties (Amer. J. Math., t. 81, 1949. p. 893-914). | MR 33093 | Zbl 0041.48302

18. Chow. _ Algebraic systems of positive cycles in an algebraic variety (Amer. J. Math., t. 82, 1950, p. 247-283). | MR 34606 | Zbl 0036.37302

19. Chow et Van Der Waerden. _ Zur algebraischen Geometrie IX (Math. Ann., t. 113, 1937, p. 692-704). | JFM 62.0772.02 | MR 1513117 | Zbl 0016.04004

20. Cohen. _ On the structure and ideal theory of complete local rings (Trans. Amer. Math. Soc, t. 59, 1946, p. 54-106). | MR 16094 | Zbl 0060.07001

21. Cohen. _ Commutative rings with restricted minimum condition (Duke Math. J. t. 17, 1950, p. 27-42). | MR 33276 | Zbl 0041.36408

22. Cohen et Seidenberg. _ Prime ideals and integral dependence (Bull. Amer. Math. Soc., t. 52, 1946, p. 252-261). | MR 15379 | Zbl 0060.07003

23. Dubreil. _ Recherches sur la valeur des exposants des composantes primaires des idéaux de polynomes (J. Math. pures et appl., t. 9, 1930, p. 231-309). | JFM 56.0170.04

24. Dubreil. _ Quelques propriétés des variétés algébriques (Exposés Herbrand, Paris, Hermann, 1935). | JFM 59.0927.02 | Zbl 0007.03105

25. Dubreil. _ La fonction caractéristique de Hilbert (Colloque d'Algèbre, et Théorie des Nombres, Paris, C. N. R. S., 1950, p. 109-114). | MR 44156 | Zbl 0040.15601

26. Grell. _ Beziehungen zwischen den Idealen verschiedener Ringe (Math. Ann., t. 97, 1927, p. 490-523). | JFM 53.0116.03 | MR 1512373

27. Grobner. _ Idealtheoretischer Aufbau deralgebraischen Geometrie (Hamb. Math. Einzehchriften, t. 30, 1941). | JFM 67.0593.01 | Zbl 0026.25005

28. Grobner. _ Algebraische Geometrie, 1949.

29. Goddard. _ Bases for the prime ideals associated with certain classes of algebraic varieties (Proc. Cambridge Phil. Soc., t. 39, 1943, p. 35-48). | MR 7619 | Zbl 0063.01651

30. Goddard. _ Prime ideals and postulation formulae (Proc. Cambridge. Phil. Soc., t. 44, 1948, p. 43-49). | MR 23094 | Zbl 0029.41303

31. Grundy. _ On integrally dependent integral domains (Phil. Trans. Roy. Soc. London, série A, t. 240, 1947, p. 295-326). | MR 23233 | Zbl 0029.10701

32. Grundy. _ A generalization of additive ideal theory (Proc. Cambridge Phil. Soc., t. 38, 1942, p. 241-279). | MR 7392 | Zbl 0060.06814

33. Hasse et Schmidt. _ Die Struktur diskret bewerteter Körper (J. Reine, Angew. Math., t. 170, 1934, p. 4-63). | JFM 59.0154.03 | Zbl 0008.05202

34. Hilbert. _ Uber die Theorie der algebraischen Formen (Math. Ann. t. 36, 1898, p. 473-534). | JFM 22.0133.01 | MR 1510634

35. Hopkins. _ Rings with minimum condition for left ideals (Ann. of Math., t. 40, 1939, p. 712-730). | JFM 65.0088.02 | Zbl 0022.10602

36. Igusa. _ On the algebraic geometry of Weil and Chevalley (J. Math. Soc. Japan, t. 1, 1949, p. 198-201). | MR 31771 | Zbl 0039.16601

37. Iwasawa. _ Der Bezoutsche Satz in zweifach projektiven Räumen (Proc. Japan Acad., t. 21, 1949, p. 213-222). | MR 31772 | Zbl 0063.02998

38. Iwasawa. _ Zur theorie der algebraischen Korrespondenzen (Proc. Japan Acad., t. 21, 1949, p. 204-212). | Zbl 0063.02997

39. Iwasawa. _ Zur theorie der algebraischen Korrespondenzen (Proc. Japan Acad., t. 21, 1949, p. 411-418). | Zbl 0063.02997

40. Jacobson. _ Theory of rings (Math. Surveys, New-York, 1943). | MR 8601

41. Jacobson. _ Radical and semi simplicity for arbitrary rings (Amer. J. Math., t. 67, 1945, p. 300-320). | MR 12271 | Zbl 0060.07305

42. Krull. _ Idealtheorie (Ergebnisse, IV, 3, Berlin, 1935). | JFM 61.0113.01 | Zbl 0011.19702

43. Krull. _ Zum Dimensions begriff der Idealtheorie (Math. Z., t. 42, 1937, p. 745-766). | JFM 63.0879.02 | Zbl 0017.14901

44. Krull. _ Pozreihenringe (Math. Z., t. 43, 1938, p. 768-782). | MR 1545748 | Zbl 0019.14802

45. Krull. _ Dimensionsthoerie in Stellenringen (J. Reine Angew. Math., t. 179, 1938, p. 204-226). | JFM 64.0078.02

46. Krull. _ Enzyklopädie der mathematischen Wissenschaften, I, 1, 5 (Leipzig, Teubner, 1939). | Zbl 0024.00803

47. Krull. _ Funktionaldeterminanten und Diskriminanten bei Polynomen in mehreren Unbestimmten (Monatsh. Math. Phys., t. 48, 1939, p. 353-368 et t. 50, 1942, p. 234-256). | MR 609 | Zbl 0021.29302

48. Krull. _ Parameterspezialisierung in Polynomringen (Arch. Math., t. 1, 1948, p. 56-64 et 129-137). | MR 26640 | Zbl 0034.16701

49. Macaulay. _ The algebraic theory of modular systems (Cambridge Tracts, 19, Cambridge, 1916). | JFM 46.0167.01 | Zbl 0802.13001

50. Mac Lane. _ Subfields and automorphism groups of p-adic fields (Ann. of Math., t. 40, 1939, p. 423-442). | MR 1503470 | Zbl 0021.00501

51. Muhly. _ Independent integral bases and a characterization of normal surfaces (Trans. Amer. Math. Soc., t. 54, 1943, p. 340-360). | MR 8914 | Zbl 0063.04129

52. Nagata. _ On the structure of complete local rings (Nagoya Math. J., t. 1, 1950, p. 63-70). | MR 41829 | Zbl 0039.26303

53. M. Noether. _ Zur Grundlegung der Theorie der algebraischen Raum-kurven (Abh. Brelin. Akad., 1882). | JFM 15.0684.01

54. Okugawa. _ Remarks on O. Zariski's paper (Mem. Coll. Sci. Kyoto Imp. Univ., série A, t. 23, 1941, p. 437-444). | MR 15842 | Zbl 0063.06019

55. Perron. _ Studien über die Vielfachheitbegriff und den Bezoutschen Satz (Math. Z., t.. 49, 1944, p. 654-680). | MR 11569 | Zbl 0028.41702

56. Samuel. _ On universal mappings and free topological groups (Bull. Amer. Math. Soc., t. 54, 1948, p. 591-598). | MR 25152 | Zbl 0031.41702

57. Samuel. _ Une généralisation des polynomes de Hilbert (C. R. Acad. Sc., t. 225, 1947, p. 1111-1113). | MR 23234 | Zbl 0029.10602

58. Samuel. _ Sur les anneaux locaux (C. R. Acad. Sc., t. 225, 1947, p. 1244-1245). | MR 23235 | Zbl 0029.24602

59. Samuel. _ Multiplicités des composantes excédentaires d'intersection (C. R. Acad. Sc., t. 228, 1949, p. 158-159). | MR 30229 | Zbl 0034.08801

60. Samuel. _ Multiplicités des composantes singulières d'intersection (C. R. Acad. Sc., t. 228, 1949, p. 292-294). | MR 30230 | Zbl 0033.20602

61. Samuel. _ Multiplicités d'intersection en Géométrie algébrique (Colloque d'Algèbre et Théorie des Nombres, Paris, C. N. R. S., 1950, p. 123-124). | Zbl 0040.08103

62. Samuel. _ Multiplicités des composantes singulières d'intersection (Colloque de Géométrie algébrique, Liège, Thone, 1950, p. 87-90). | Zbl 0037.22202

63. Samuel. _ Sur la notion de multiplicité en Algèbre et en Géométrie algébrique (J. Math. pures et appl., t. 30, 1951, p. 159). | MR 48103 | Zbl 0044.02701

64. Samuel. _ Sur les variétés algébroïdes (Ann. Inst. Fourier, t. 2, 1950, p. 147-160). | Numdam | MR 45414 | Zbl 0044.26502

65. Schilling. _ Valuation theory (Math. Surveys, New-York, 1950).

66. Seidenberg. _ The hyperplane sections of normal varieties (Trans. Amer. Math. Soc., t. 63, 1950, p. 357-386). | MR 37548 | Zbl 0040.23501

67. Severi. _ Una proprieta delle forme algebriche prive di punti multipli (Rend. Lincei, vol. V, t. 15, 1906, p. 691-696). | JFM 37.0131.01

68. Severi. _ Sulla varieta che representa gli spazi subordinati... (Ann. di Mat., vol. III, t. 24, 1915, p. 89-120). | JFM 45.0915.03

69. Severi. _ Uber die Grundlagen der algebraischen Geometrie (Abh. Hamburg Univ., t. 9, 1933, p. 335-364). | JFM 59.0604.02 | Zbl 0007.07501

70. Snapper. _ Polynomial matrices... (Amer. J. Math., t. 69, 1947, p. 299-326 et 622-652). | Zbl 0036.29001

71. Sperner. _ Ueber einem kombinatorischen Satz von Macaulay (Abh. Hamburg Univ., t. 7, 1930, p. 149-163). | JFM 55.0663.01

72. Terpstra. _ Over zekere ongemengde Idealen (Thèse, Amsterdam, 1946).

73. Teichmuller. _ Diskret bewertete peifekte Körper mit unvollkommenen Restklassenkörper (J. Reine Angew. Math., t. 176, 1937, p. 141-152). | JFM 62.1114.01 | Zbl 0016.05103

74. Todd. _ On algebraic curve branches (J. London Math. Soc., t. 21, 1946, p. 223-240). | MR 20801 | Zbl 0063.07800

75. Uzkov. _ An algebraic lemma and the normalization theorem of E. Noether (Mat. Sbornik, N. S., t. 22 (64), 1948 (en russe), p. 349-350; Math. Rev., t. 10, 1949, p. 562). | MR 24888 | Zbl 0038.15502

76. Uzkov. _ On rings of quotients of commutative rings (Mat. Sbornik, N. S., t. 22 (64), 1948 (en russe), p. 439-441; Math. Rev., t. 10, 1949, p. 97). | MR 26041 | Zbl 0035.01903

77. Van Der Waerden _ Moderne Algebra, 2e édition | JFM 63.0082.06 | Zbl 0055.02502

78 Van Der Waerden _ Der Multiplizitätsbegriff der algebraischen Geometrie (Math Ann , t 97, 1927, p 756-774) | JFM 53.0103.02 | MR 1512387

79 Van Der Waerden _ On Hilberts function... (Proc. Kon. Acad. Amsterdam, t 31, 1928, p 749-770) | JFM 54.0190.02

80 Van Der Waerden _ Eine Verallgemeinerung des Bézoutschen Theorems (Math. Ann., t. 99, 1928, p. 497-541). | JFM 54.0141.01 | MR 1512464

81. Van Der Waerden. _ Einführung in die algebraische Geometrie (New-York, Dover, 1945). | MR 15836 | Zbl 0264.14001

82. Van Der Waerden. _ Die Bedeutung des Bewertungsbegriff für die algebraische Geometrie (J. ber. Deutsch. Math. Verein., t. 52, 1942, p. 161-172). | MR 8467 | Zbl 0027.24402

83. Van Der Waerden. _ Uebei einfache Punkte von algebraischen Mannigfaltigkeiten (Math. Z., t. 51, 1948, p. 497-501). | MR 29523 | Zbl 0031.17902

84. Weil. _ Foundations of algebraic geometry (Amer. Math. Soc. Coll. Publ., New-York, 1946). | MR 23093 | Zbl 0063.08198

85. Zariski. _ Some results in the arithmetic theory of algebraic varieties (Amer. J. Math., t. 61, 1939, p. 249-294). | JFM 65.0118.02 | MR 1507376

86. Zariski. _ The reduction of singularities of an algebraic surface (Ann. of Math., t. 40, 1939, p. 639-689). | MR 159 | Zbl 0021.25303

87. Zariski. _ Algebraic varieties over ground fields of characteristic zero (Amer. J. Math., t. 62, 1940, p. 187-221). | JFM 66.0792.01 | MR 611

88. Zariski. _ Local uniformization of algebraic varieties (Ann. of Math t. 41, 1940, p. 852-896). | JFM 66.1327.02 | MR 2864 | Zbl 0025.21601

89. Zariski. _ Normal varieties and birational correspondences (Bull. Amer Math. Soc., t. 48, 1942, p. 402-413). | MR 6451 | Zbl 0063.08388

90. Zariski. _ A simplified proof for the resolution of singularities of an algebraic surface (Ann. of Math., t. 43, 1942, p. 583-593). | MR 6851 | Zbl 0063.08389

91. Zariski. _ Foundations of a general theory of birational correspondences (Trans. Amer. Math. Soc., t. 53, 1943, p. 490-542). | MR 8468 | Zbl 0061.33004

92. Zariski. _ Reduction of singularities of algebraic three dimensional varieties (Ann. of Math., t. 45, 1944, p. 472-542). | MR 11006 | Zbl 0063.08361

93. Zariski. _ Generalized semi-local rings (Summa Bras. Math., t. 1, 1946, p. 169-195). | MR 22835 | Zbl 0063.08392

94. Zariski. _ The concept of a simple point of an abstract algebraic variety (Trans. Amer. Math. Soc., t. 62, 1947, p. 1-52). | MR 21694 | Zbl 0031.26101

95. Zariski. _ Analytical irreducibility of normal varieties (Ann. of Math. t. 49, 1948, p. 352-361). | MR 24158 | Zbl 0037.22701

96. Zariski. _ A simple analytical proof of a fundamental property of birational transformations (Proc. Nat. Acad. Sc., t. 35, 1949, p. 62-66). | MR 28056 | Zbl 0037.16401

97. Zariski. _ Quelques questions concernant la théorie des fonctions holomorphes sur une variété algébrique (Colloque d'Algèbre et Théorie des Nombres, Paris, C. N. R. S., 1950, p. 129-133). | MR 43500 | Zbl 0041.48102

98. Zariski. _ Sur la normalité analytique des variétés normales (Ann. Inst. Fourier, t. 2, 1950, p. 161-166). | Numdam | MR 45413 | Zbl 0044.26601