On the compositum of two power series rings
HTML articles powered by AMS MathViewer
- by Shreeram S. Abhyankar, William Heinzer and Sylvia Wiegand PDF
- Proc. Amer. Math. Soc. 112 (1991), 629-636 Request permission
Abstract:
This paper concerns subrings of the bivariate power series ring over a field.References
- Shreeram Abhyankar, Two notes on formal power series, Proc. Amer. Math. Soc. 7 (1956), 903–905. MR 80647, DOI 10.1090/S0002-9939-1956-0080647-9
- Shreeram S. Abhyankar, Algebraic geometry for scientists and engineers, Mathematical Surveys and Monographs, vol. 35, American Mathematical Society, Providence, RI, 1990. MR 1075991, DOI 10.1090/surv/035 S. Abhyankar and W. Heinzer, Integral closure and ramification of prime ideals in infinite algebraic field extensions, J. Algebra (to appear).
- S. S. Abhyankar and T. T. Moh, On analytic independence, Trans. Amer. Math. Soc. 219 (1976), 77–87. MR 414546, DOI 10.1090/S0002-9947-1976-0414546-4
- R. Berger, R. Kiehl, E. Kunz, and Hans-Joachim Nastold, Differentialrechnung in der analytischen Geometrie, Lecture Notes in Mathematics, No. 38, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224870
- Claude Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, Mathematical Surveys, No. VI, American Mathematical Society, New York, N. Y., 1951. MR 0042164
- William Heinzer and Sylvia Wiegand, Prime ideals in two-dimensional polynomial rings, Proc. Amer. Math. Soc. 107 (1989), no. 3, 577–586. MR 982402, DOI 10.1090/S0002-9939-1989-0982402-3 M. F. Huang, On the algebraic closure of the field of meromorphic functions over an algebraically closed field of characteristic, Ph.D. Thesis, Purdue University, 1968.
- Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975, DOI 10.1007/978-3-663-14074-0
- Hideyuki Matsumura, Commutative algebra, 2nd ed., Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. MR 575344
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
- F. J. Rayner, An algebraically closed field, Glasgow Math. J. 9 (1968), 146–151. MR 234941, DOI 10.1017/S0017089500000422
- Friedrich Karl Schmidt, Mehrfach perfekte Körper, Math. Ann. 108 (1933), no. 1, 1–25 (German). MR 1512831, DOI 10.1007/BF01452819
- Philip B. Sheldon, How changing $D[[x]]$ changes its quotient field, Trans. Amer. Math. Soc. 159 (1971), 223–244. MR 279092, DOI 10.1090/S0002-9947-1971-0279092-5
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 629-636
- MSC: Primary 13J05; Secondary 13J10, 13J15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057740-8
- MathSciNet review: 1057740