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Sur les séries formelles restreintes. (French) Zbl 0196.31101

Ausführliche und erweiterte Darstellung von bereits früher angekündigten Resultaten [C. R. Acad. Sci., Paris 255, 227–228 (1962; Zbl 0111.24802); 255, 439–441 (1962; Zbl 0128.26201); 256, 4808–4810 (1963; Zbl 0128.26103)].

MSC:

13F25 Formal power series rings
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References:

[1] ANDREOTTI (A.) und SALMON (P.) .- Anelli con unica decomponibilità in fattori primi ed un problema di intersezioni complete, Monatshefte für Math. , t. 61, 1957 , p. 97-142. MR 21 #3415 | Zbl 0079.15002 · Zbl 0079.15002
[2] AUSLANDER (M.) and BUCHSBAUM (D. A.) .- Unique factorization in regular local rings , Proc. Nat. Acad. Sc. U. S. A., t. 45, 1959 , p. 733-734. MR 21 #2669 | Zbl 0084.26504 · Zbl 0084.26504
[3] BUCHSBAUM (D. A.) .- Some remarks on factorization in power series rings , J. of Math. and Mech., t. 10, 1961 , p. 749-753. MR 23 #A1666 | Zbl 0115.26203 · Zbl 0115.26203
[4] BOURBAKI (N.) .- Algèbre commutative , Chap. 1-2, 3-4.- Paris, Hermann, 1961 (Act. scient. et ind., 1290 - 1293 ; Bourbaki, 27-28).
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[6] GROTHENDIECK (A.) et DIEUDONNÉ (J.) .- Éléments de géométrie algébrique .- Paris, Presses universitaires de France, 1960 (Institut des Hautes Études scientifiques, Publications mathématiques, 4). Numdam | Zbl 0118.36206 · Zbl 0118.36206
[7] GROTHENDIECK (A.) .- Séminaire de géométrie algébrique . Notes prises par un groupe d’auditeurs. Exposés 1 à 13. Bures-sur-Yvette, Institut des Hautes Études scientifiques, 1960 - 1962 (multigraphié).
[8] KRULL (W.) .- Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensions-theorie, Math. Z. , t. 54, 1951 , p. 354-387. MR 13,903c | Zbl 0043.03802 · Zbl 0043.03802
[9] LEFSCHETZ (S.) .- On certain numerical invariants of algebraic varieties , Trans. Amer. math. Soc., t. 22, 1921 , p. 327-363. MR 1501178 | JFM 48.0428.03 · JFM 48.0428.03
[10] NAGATA (M.) .- A remark on the unique factorization theorem , J. Math. Soc. Japan, t. 9, 1957 , p. 143-145. Article | MR 18,869a | Zbl 0079.05405 · Zbl 0079.05405
[11] NAGATA (M.) .- Local rings .- New York, London, Interscience Publishers, 1962 (Interscience Tracts in pure and applied Mathematics, 13). MR 27 #5790 | Zbl 0123.03402 · Zbl 0123.03402
[12] SALMON (P.) .- Sur les séries formelles restreintes , C. R. Acad. Sc. Paris, t. 255, 1962 , p. 227-229. MR 26 #2464 | Zbl 0111.24802 · Zbl 0111.24802
[13] SALMON (P.) .- Sur les séries restreintes et convergentes , C. R. Acad. Sc. Paris, t. 255, 1962 , p. 439-441. MR 26 #150 | Zbl 0128.26201 · Zbl 0128.26201
[14] SALMON (P.) .- Sur les complétés des anneaux noethériens et les séries formelles restreintes , C. R. Acad. Sc. Paris, t. 256, 1963 , p. 4808-4810. MR 27 #2525 | Zbl 0128.26103 · Zbl 0128.26103
[15] SAMUEL (P.) .- On unique factorization domains , Illinois J. Math., t. 5, 1961 , p. 1-17. Article | MR 22 #12121 | Zbl 0147.29202 · Zbl 0147.29202
[16] SAMUEL (P.) .- Sur les anneaux factoriels , Bull. Soc. math. France, t. 89, 1961 , p. 155-173. Numdam | MR 25 #3046 | Zbl 0101.27305 · Zbl 0101.27305
[17] SERRE (J.-P.) .- Algèbre locale, multiplicités . Cours au Collège de France, 1957 - 1958 , rédigé par P. GABRIEL (multigraphié). Zbl 0091.03701 · Zbl 0091.03701
[18] SEVERI (F.) .- Una proprietà delle forme algebriche prive di punti multipli , Atti della Accad. dei Lincei, Rendic., Série 5, t. 15, 1906 , 2e sem., p. 691-696. JFM 37.0131.01 · JFM 37.0131.01
[19] ZARISKI (O.) and SAMUEL (P.) .- Commutative algebra , Vol. 1 and 2.- Princeton, Van Nostrand, 1958 - 1960 . Zbl 0121.27801 · Zbl 0121.27801
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