On the structure and ideal theory of complete local rings
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- by I. S. Cohen PDF
- Trans. Amer. Math. Soc. 59 (1946), 54-106 Request permission
References
- Claude Chevalley, On the theory of local rings, Ann. of Math. (2) 44 (1943), 690–708. MR 9603, DOI 10.2307/1969105
- I. S. Cohen and A. Seidenberg, Prime ideals and integral dependence, Bull. Amer. Math. Soc. 52 (1946), 252–261. MR 15379, DOI 10.1090/S0002-9904-1946-08552-3
- Helmut Hasse, Kurt Hensels entscheidender Anstoss zur Entdeckung des Lokal-Global-Prinzips, J. Reine Angew. Math. 209 (1962), 3–4 (German). MR 139510, DOI 10.1515/crll.1962.209.3 W. Krull, Idealtheorie, Ergebnisse der Mathematik und ihrer Grenzgebiete, IV 3, Berlin, 1935. —, Zum Dimensionsbegriff der Idealtheorie (Beiträge zur Arithmetik kommutativer Integritätsbereiche, III), Math. Zeit. vol. 42 (1937) pp. 745-766.
- Wolfgang Krull, Beiträge zur Arithmetik kommutativer Integritätsbereiche, Math. Z. 43 (1938), no. 1, 768–782 (German). MR 1545748, DOI 10.1007/BF01181119 —, Dimensionstheorie in Stellenringen, J. Reine Angew. Math. vol. 179 (1938) pp. 204-226. F. S. Macaulay, The algebraic theory of modular systems, Cambridge Tracts in Mathematics and Mathematical Physics, vol. 19, Cambridge, 1916.
- Saunders Mac Lane, Subfields and automorphism groups of $p$-adic fields, Ann. of Math. (2) 40 (1939), no. 2, 423–442. MR 1503470, DOI 10.2307/1968931
- N. H. McCoy, Remarks on divisors of zero, Amer. Math. Monthly 49 (1942), 286–295. MR 6150, DOI 10.2307/2303094
- Walther Rückert, Zum Eliminationsproblem der Potenzreihenideale, Math. Ann. 107 (1933), no. 1, 259–281 (German). MR 1512800, DOI 10.1007/BF01448893 O. Teichmüller, Diskret bewertete perfekte Körper mit unvollkommenen Restklassenkörper, J. Reine Angew. Math. vol. 176 (1937) pp. 141-152.
- Oscar Zariski, Algebraic varieties over ground fields of characteristic zero, Amer. J. Math. 62 (1940), 187–221. MR 611, DOI 10.2307/2371447
- Oscar Zariski, Foundations of a general theory of birational correspondences, Trans. Amer. Math. Soc. 53 (1943), 490–542. MR 8468, DOI 10.1090/S0002-9947-1943-0008468-9
Additional Information
- © Copyright 1946 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 59 (1946), 54-106
- MSC: Primary 09.1X
- DOI: https://doi.org/10.1090/S0002-9947-1946-0016094-3
- MathSciNet review: 0016094