On the compositum of two power series rings
Authors:
Shreeram S. Abhyankar, William Heinzer and Sylvia Wiegand
Journal:
Proc. Amer. Math. Soc. 112 (1991), 629636
MSC:
Primary 13J05; Secondary 13J10, 13J15
MathSciNet review:
1057740
Fulltext PDF Free Access
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
(18,277a), http://dx.doi.org/10.1090/S00029939195600806479
 [A2]
Shreeram
S. Abhyankar, Algebraic geometry for scientists and engineers,
Mathematical Surveys and Monographs, vol. 35, American Mathematical
Society, Providence, RI, 1990. MR 1075991
(92a:14001)
 [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
(54 #2647), http://dx.doi.org/10.1090/S00029947197604145464
 [BKKN]
R.
Berger, R.
Kiehl, E.
Kunz, and H.J.
Nastold, Differentialrechnung in der analytischen Geometrie,
Lecture Notes in Mathematics, No. 38, SpringerVerlag, Berlin, 1967
(German). MR
0224870 (37 #469)
 [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
(13,64a)
 [HW]
William
Heinzer and Sylvia
Wiegand, Prime ideals in twodimensional
polynomial rings, Proc. Amer. Math. Soc.
107 (1989), no. 3,
577–586. MR
982402 (90b:13010), http://dx.doi.org/10.1090/S00029939198909824023
 [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
(88e:14025)
 [M]
Hideyuki
Matsumura, Commutative algebra, 2nd ed., Mathematics Lecture
Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading,
Mass., 1980. MR
575344 (82i:13003)
 [N]
Masayoshi
Nagata, Local rings, Interscience Tracts in Pure and Applied
Mathematics, No. 13, Interscience Publishers a division of John Wiley &
Sons New YorkLondon, 1962. MR 0155856
(27 #5790)
 [R]
F.
J. Rayner, An algebraically closed field, Glasgow Math. J.
9 (1968), 146–151. MR 0234941
(38 #3255)
 [S]
Friedrich
Karl Schmidt, Mehrfach perfekte Körper, Math. Ann.
108 (1933), no. 1, 1–25 (German). MR
1512831, http://dx.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
(43 #4818), http://dx.doi.org/10.1090/S00029947197102790925
 [A1]
 S. Abhyankar, Two notes on formal power series, Proc. Amer. Math. Soc. 7 (1956), 903905. MR 0080647 (18:277a)
 [A2]
 , Algebraic geometry for scientists and engineers, Surveys and Monographs of the Amer. Math. Soc., no. 35, Amer. Math. Soc., Providence, RI, 1990. MR 1075991 (92a:14001)
 [AH]
 S. Abhyankar and W. Heinzer, Integral closure and ramification of prime ideals in infinite algebraic field extensions, J. Algebra (to appear).
 [AM]
 S. Abhyankar and T. Moh, On analytic independence, Trans. Amer. Math. Soc. 219 (1976), 7787. MR 0414546 (54:2647)
 [BKKN]
 R. Berger, R. Kiehl, E. Kunz, and J.J. Nastold, Differentialrechnung In Der Analytischen Geometrie, Lecture Notes in Math., vol. 38, SpringerVerlag, New York, 1967. MR 0224870 (37:469)
 [C]
 C. Chevalley, Introduction to the theory of algebraic functions of one variable, Surveys and Monographs of the Amer. Math. Soc., no. 6, Amer. Math. Soc., Providence, RI, 1951. MR 0042164 (13:64a)
 [HW]
 W. Heinzer and S. Wiegand, Prime ideals in twodimensional polynomial rings, Proc. Amer. Math. Soc. 107 (1989), 577586. MR 982402 (90b:13010)
 [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]
 E. Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Viewig & Sohn, Braunschweig, 1986. MR 864975 (88e:14025)
 [M]
 H. Matsumura, Commutative algebra, Benjamin/Cummings, Reading, MA, 1980. MR 575344 (82i:13003)
 [N]
 M. Nagata, Local rings, Interscience, New York, 1962. MR 0155856 (27:5790)
 [R]
 F. J. Rayner,, An algebraically closed field, Glasgow Math. J. 9 (1968), 146151. MR 0234941 (38:3255)
 [S]
 F. K. Schmidt, Mehrfach perfekte Korper, Math. Ann. 108 (1933), 125. MR 1512831
 [Sh]
 P. B. Sheldon, How changing changes its quotient field, Trans. Amer. Math. Soc. 159 (1971), 223244. MR 0279092 (43:4818)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199110577408
PII:
S 00029939(1991)10577408
Keywords:
Completion,
Henselian,
Noetherian,
power series,
transcendental
Article copyright:
© Copyright 1991 American Mathematical Society
