5. Juli 2004. U. Schoenwaelder; http://www.math.rwth-aachen.de/∼Ulrich.Schoenwaelder HB = Hochschulbibl. RWTH, HBZ = http://www.hbz-nrw.de/ (HBZ-CD-ROM Online), MB = Mathematikbibl., DB = Didaktikbibl. (Winter), EB = Erziehungswiss. Bibl., FH = Bibl. Fachhochschule Aachen, FL = Fernleihe, IB = Informatikbibliothek, IB Nr. = Institutsbibliothek Nr., LB = HB– Lehrbuchsammlung, LS = HB–Lesesaal

Literatur zur Bewertungstheorie (insbes. in der Algebraischen Zahlentheorie)

[1] J. Alajbegović and J. Močkoř. Approximation Theorems in Commutative Algebra. Classical and Categorical Methods. Mathematics and Its Applications (East European Series) 59. Kluwer Acad. Publ., 1992. MB: 16716. Ch. 1: Approximation theorems for valuations on fields.

[2] E. Artin. Algebraic Numbers and Algebraic Functions. Gordon & Breach, 1967. MB: 4297. Part One: General valuation theory.

[3] P. M. Cohn. Lectures on Algebraic Numbers and Algebraic Fields. Queen’s papers in pure and applied mathematics 15. Kingston, Ont.: Queen’s Univ., 1969. MB: 5596.

[4] P. M. Cohn. Algebraic Numbers and Algebraic Functions. Chapman & Hall, 1991. HB: Bf 9323.

[5] Otto Endler. Valuation Theory. Universitext. Springer–Verlag, 1972. MB: 7279.

[6] I. B. Fesenko and S. V. Vostokov. Local Fields and Their Extensions: A Constructive Approach. Translations of Mathematical Monographs 121. AMS, 1993. ISBN 0-8218-4613-2. MB: 16871. Hensel’s Lemma: p. 30. Formal power series: p. 161 ff.

[7] R. Gilmer. Multiplicative Ideal Theory. Pure and Applied Mathematics. A Series of Monographs and Textbooks. Marcel Dekker, 1972. MB: 6928. Ch. I.§7: Invertible ideals. Ch. III: Valuation theory.

[8] J. K. Goldhaber and G. Ehrlich. Algebra. Macmillan, London, 1970.

[9] F. Halter-Koch. Ideal Systems, An Introduction to Multiplicative Ideal Theory. Pure and Applied Mathematics 211. Dekker, 1998. MB:. ISBN 0-8247-0186-0. Derives valuation theory in a purely multiplicative form for the first time.

[10] H. Hasse. Zahlentheorie. Akademie–Verlag, Berlin, 1949,^{2}1963, ^{3}1969. MB: 411, 2528. ”Blauer Hasse“. Kap. II: Theorie der bewerteten Körper. Kap. III: Die Grundlagen der Arithmetik in algebraischen Zahlkörpern.

[11] R. L. Long. Algebraic Number Theory. Marcel Dekker, 1977. MB: 9555. Bewertungen.

[12] P. J. McCarthy. Algebraic Extensions of Fields. Waltham: Blaisdell; New York: Chelsea; Dover, 1966; ^{2}1976; 1991. MB: 3767; 9604; -. Valuation Theory. Tel. Rev.: Amer. Math. Monthly 100(1):1993, 96.

[13] J. Milne. Algebraic Number Theory. Vorlesungsskript. Internet, August 14 1992. uschoenw > VorlesungAlgZth/jmilne. algebraicnumbertheory.dvi. Siehe S. 51 ff und 100 ff.

[14] Paulo Ribenboim. The Theory of Classical Valuations. Springer Monographs in Mathematics. Springer, 1999. MB: 18840. ISBN 0-387-98525-5.

[15] J.-P. Serre. Local Fields. GTM 67. Springer–Verlag, 1979. MB: 10679. Ch. 1: Discrete Valuation Rings and Dedekind Domains. Ch. 2: Completion.

[16] E. Weiss. Algebraic Number Theory. International series in pure and applied mathematics. McGraw–Hill, 1963. MB: 2628. Beginnt mit Bewertungstheorie.