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References
Abhyankar, S.: On the ramification of algebraic functions. Am. J. Math.77, 575–592 (1955).
—— Local uniformization on algebraic surfaces over ground fields of characteristicp ≠ 0. Ann. Math.63, 491–526 (1956). Corrections, Ann. Math.78, 202–203 (1963).
—— On the valuations centered in a local domain. Am. J. Math.78, 321–348 (1956).
—— Simultaneous resolution for algebraic surfaces. Am. J. Math.78, 761–790 (1956).
—— On the field of definition of a nonsingular birational transform of an algebraic surface. Ann. Math.65, 268–281 (1957).
—— Ramification theoretic methods in algebraic geometry. Princeton: Princeton University Press 1959.
—— Uniformization inp-cyclic extensions of algebraic surfaces over ground fields of characteristicp. Math. Ann.153, 81–96 (1964).
——, andO. Zariski: Splitting of valuations in extensions of local domain. Proc. Nat. Acad. Sci. U.S.41, 84–90 (1955).
Chevalley, C.: On the theory of local rings. Ann. Math.44, 690–708 (1943).
Cohen, I. S.: On the structure and ideal theory of complete local rings. Trans. Am. Math. Soc.57, 54–106 (1946).
Jung, H. W. E.: Darstellung der Funktionen eines algebraischen Körpers zweier unabhängigen Veränderlichen in der Umgebung einer Stelle. J. reine angew. Math.133, 289–314 (1908).
Krull, W.: Allgemeine Bewertungstheorie. J. reine angew. Math.167, 160–196 (1932).
—— Dimensionstheorie in Stellenringe. J. reine angew. Math.179, 204–226 (1938).
—— Der allgemeine Diskriminantensatz. Math. Z.45, 1–19 (1939).
Nagata, M.: Note on a chain condition for prime ideals. Mem. Coll. Sci. Univ. Kyoto32, 85–90 (1959).
—— Local Rings. New York: Interscience Publishers 1962.
Pontrijagin, L.: Topological Groups. Princeton: Princeton University Press 1952.
Sakuma, M.: Existence theorems of valuations centered in a local domain with preassigned dimension and rank. J. Sci. Hiroshima University21, 61–67 (1957).
van der Waerden, B. L.: Modern Algebra, vol. I. New York: Frederick Unger Publishing Company 1949.
—— Modern Algebra, vol. II. New York: Frederick Unger Publishing Company 1950.
Zariski, O.: A simple analytic proof of a fundamental property of birational transformations. Proc. Nat. Acad. Sci. U.S.35, 62–66 (1949).
—— Le problème de la réduction des singularités d'un variété algébrique. Bull. sci. math.78, 1–10 (1954).
——, andP. Samuel: Commutative Algebra, vol. I. Princeton: Van Nostrand 1958.
—— —— Commutative Algebra, vol. II. Princeton: Van Nostrand 1960.
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Abhyankar, S. Uniformization of Jungian local domains. Math. Ann. 159, 1–43 (1965). https://doi.org/10.1007/BF01359903
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DOI: https://doi.org/10.1007/BF01359903