On the compositum of two power series rings

Authors:
Shreeram S. Abhyankar, William Heinzer and Sylvia Wiegand

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

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper concerns subrings of the bivariate power series ring over a field.

**[A1]**Shreeram Abhyankar,*Two notes on formal power series*, Proc. Amer. Math. Soc.**7**(1956), 903–905. MR**0080647**, https://doi.org/10.1090/S0002-9939-1956-0080647-9**[A2]**Shreeram S. Abhyankar,*Algebraic geometry for scientists and engineers*, Mathematical Surveys and Monographs, vol. 35, American Mathematical Society, Providence, RI, 1990. MR**1075991****[AH]**S. Abhyankar and W. Heinzer,*Integral closure and ramification of prime ideals in infinite algebraic field extensions*, J. Algebra (to appear).**[AM]**S. S. Abhyankar and T. T. Moh,*On analytic independence*, Trans. Amer. Math. Soc.**219**(1976), 77–87. MR**0414546**, https://doi.org/10.1090/S0002-9947-1976-0414546-4**[BKKN]**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****[C]**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****[HW]**William Heinzer and Sylvia Wiegand,*Prime ideals in two-dimensional polynomial rings*, Proc. Amer. Math. Soc.**107**(1989), no. 3, 577–586. MR**982402**, https://doi.org/10.1090/S0002-9939-1989-0982402-3**[H]**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.**[K]**Ernst Kunz,*Kähler differentials*, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR**864975****[M]**Hideyuki Matsumura,*Commutative algebra*, 2nd ed., Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. MR**575344****[N]**Masayoshi Nagata,*Local rings*, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. MR**0155856****[R]**F. J. Rayner,*An algebraically closed field*, Glasgow Math. J.**9**(1968), 146–151. MR**0234941**, https://doi.org/10.1017/S0017089500000422**[S]**Friedrich Karl Schmidt,*Mehrfach perfekte Körper*, Math. Ann.**108**(1933), no. 1, 1–25 (German). MR**1512831**, https://doi.org/10.1007/BF01452819**[Sh]**Philip B. Sheldon,*How changing 𝐷[[𝑥]] changes its quotient field*, Trans. Amer. Math. Soc.**159**(1971), 223–244. MR**0279092**, https://doi.org/10.1090/S0002-9947-1971-0279092-5

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1057740-8

Keywords:
Completion,
Henselian,
Noetherian,
power series,
transcendental

Article copyright:
© Copyright 1991
American Mathematical Society