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Constructions in algebra
Author:
A. Seidenberg
Journal:
Trans. Amer. Math. Soc. 197 (1974), 273-313
MSC:
Primary 13A15; Secondary 02E10
MathSciNet review:
0349648
Full-text PDF Free Access
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Additional Information
Abstract: It is shown how to construct a primary decomposition and to find the associated prime ideals of a given ideal in a polynomial ring. This is first done from a classical, and then from a strictly constructivist, point of view.
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- [1]
- G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1926), 736-788. MR 1512302
- [2]
- W. Krull, Parameterspezialisierung in Polynomringen, Arch. Math. 1 (1948), 56-64. MR 10, 178. MR 0026640 (10:178f)
- [3]
- -, Parameterspezialisiening in Polynomringen. II. Das Grundpolynom, Arch. Math. 1 (1948), 129-137. MR 11, 310. MR 0032587 (11:310g)
- [4]
- A. Seidenberg, The hyperplane sections of normal varieties, Trans. Amer. Math. Soc. 69 (1950), 357-386. MR 12, 279. MR 0037548 (12:279a)
- [5]
- -, Construction of the integral closure of a finite integral domain, Rend. Sem. Mat. Fis. Milano 40 (1970), 100-120. (Italian) MR 45 #3396. MR 0294327 (45:3396)
- [6]
- -, On the impossibility of some constructions in polynomial rings, Atti del Convegno Internazionale di Geometria, Accademia Nazionale dei Lincei, 1973, pp. 77-85.
- [7]
- -, On the length of a Hilbert ascending chain, Proc. Amer. Math. Soc. 29 (1971), 443-450. MR 43 #6193. MR 0280473 (43:6193)
- [8]
- -, Constructive proof of Hilbert's theorem on ascending chains, Trans. Amer. Math. Soc. 174 (1972), 305-312. MR 0314829 (47:3379)
- [9]
- G. Stolzenberg, Constructive normalization of an algebraic variety, Bull. Amer. Math. Soc. 74 (1968), 595-599. MR 37 #201. MR 0224602 (37:201)
- [10]
- B. L. van der Waerden, Eine Bemerkung über die Unzerlegbarkeit von Polynomen, Math. Ann. 102 (1930), 738-739. MR 1512605
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- -, Moderne algebra. Vol. I, 2nd rev. ed., Springer, Berlin, 1937; English transl., Ungar, New York, 1949. MR 10, 587.
- [12]
- -, Moderne algebra. Vol. II, Springer, Berlin, 1931; English transl., Ungar, New York, 1950.
- [13]
- O. Zariski and P. Samuel, Commutative algebra. Vol. I, University Series in Higher Math., Van Nostrand, Princeton, N. J., 1960. MR 22 #11006. MR 0120249 (22:11006)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1974-0349648-2
PII:
S 0002-9947(1974)0349648-2
Keywords:
Constructive mathematics,
polynomial ideals
Article copyright:
© Copyright 1974 American Mathematical Society
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