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Constructions in algebra. (English) Zbl 0356.13007


MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13A15 Ideals and multiplicative ideal theory in commutative rings
68W99 Algorithms in computer science
13C05 Structure, classification theorems for modules and ideals in commutative rings
14A05 Relevant commutative algebra
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References:

[1] Grete Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1926), no. 1, 736 – 788 (German). · JFM 52.0127.01
[2] Wolfgang Krull, Parameterspezialisierung in Polynomringen, Arch. Math. 1 (1948), 56 – 64 (German). · Zbl 0034.16701
[3] Wolfgang Krull, Parameterspezialisierung in Polynomringen. II. Das Grundpolynom, Arch. Math. (Basel) 1 (1948), 129 – 137 (German). · Zbl 0034.16801
[4] A. Seidenberg, The hyperplane sections of normal varieties, Trans. Amer. Math. Soc. 69 (1950), 357 – 386. · Zbl 0040.23501
[5] Abraham Seidenberg, Construction of the integral closure of a finite integral domain, Rend. Sem. Mat. Fis. Milano 40 (1970), 100 – 120 (English, with Italian summary). · Zbl 0218.14023
[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] A. Seidenberg, On the length of a Hilbert ascending chain, Proc. Amer. Math. Soc. 29 (1971), 443 – 450. · Zbl 0216.32802
[8] A. Seidenberg, Constructive proof of Hilbert’s theorem on ascending chains, Trans. Amer. Math. Soc. 174 (1972), 305 – 312 (1973). · Zbl 0256.13012
[9] Gabriel Stolzenberg, Constructive normalization of an algebraic variety, Bull. Amer. Math. Soc. 74 (1968), 595 – 599. · Zbl 0164.04202
[10] Bartel L. van der Waerden, Eine Bemerkung über die Unzerlegbarkeit von Polynomen, Math. Ann. 102 (1930), no. 1, 738 – 739 (German). · JFM 56.0825.05
[11] -, 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] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. · Zbl 0322.13001
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