27. Februar 2001. 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), FH = Bibl. Fachhochschule Aachen, FL = Fernleihe, IB Nr. Institutsbibliothek Nr., LB = HB–Lehrbuchsammlung, LS = HB–Lesesaal

Literatur zur Algebraischen Zahlentheorie

[1] W. A. Adams and L. J. Goldstein. Introduction to Number Theory. Prentice–Hall, Inc., 1976. MB: 9094. Quadratic fields and forms. Chapters: 1 Introduction; 2 Divisibility and Primes; 3 Congurences; 4 The Law of Quadratic Reciprocity; 5 Arithmetic Functions (5.3 The Möbius Inversion Formula); 6 A Few Diophantine Equations; 7 The Gaussian Integers; 8 Arithmetic in Quadratic Fields; 9 Factorization Theory in Quadratic Fields; 10 Applications of the Factorization Theory to Diophantine Equations; 11 The Representation of Integers by Binary Quadratic Forms.

[2] R. B. Allenby and E. J. Redfern. Introduction to Number Theory with Computing. 1989. MB: 14680.

[3] E. Artin. Algebraic Numbers and Algebraic Functions. Gordon & Breach, 1967. MB: 4297.

[4] S. I. Borewicz and I. R. Shafarevich. Zahlentheorie. Birkhäuser Verlag, 1966. MB: 3600, HB: 32 Za 5775.

[5] N. Bourbaki. Algèbre Commutative. Ch. 5: Entiers, Ch. 6: Valuations. Éléments de Mathématique XXX. Actualités Scientifiques et Industrielles 1308. Hermann, Paris, 1964. MB: 4754 c–d.

[6] Y. L. Cheung. Learning number theory with a computer algebra system. Intern. J. Math. Ed. Sci. Techn., 27(3):379–?, 1996.

[7] H. Cohen. A Course in Computational Algebraic Number Theory. GTM 138. Springer–Verlag, 1993. MB: 16831; HB: Bb 1244-138+1.

[8] H. Cohn. A Classical Invitation to Algebraic Numbers and Class Fields. Universitext. Springer–Verlag, 1978, ^{2}1988. MB: 10056. Tel. Rev.: Amer. Math. Monthly 86:1 (1979), 70.

[9] R. Dedekind. Theory of Algebraic Integers. Cambridge Mathematical Library. Cambridge University Press, 1996. MB: 17 991. Part I: Translators Introduction (pp. 1–50); Part II: Translation by John Stillwell of: R. Dedekind, Sur la Théorie des Nombres Entiers Algébriques, Gauthiers–Villars, 1877 (pp. 51–152).

[10] H. M. Edwards. Fermat’s Last Theorem. A Genetric Introduction to Algebraic Number Theory. GTM 50. Springer–Verlag, 1977. MB: 9404.

[11] A. Fröhlich and M. J. Taylor. Algebraic Number Theory. Cambridge Studies in Advanced Mathematics 27. Cambridge University Press, 1991. MB: 16171.

[12] E. Grosswald. Topics from the Theory of Numbers. Birkhäuser, ^{2}1984. MB: 12306. Ch. 10: The arithmetic of number fields; Ch. 11: Ideal theory; Ch. 14: Fermat’s equation.

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

[14] K. Ireland and M. Rosen. A Classical Introduction to Algebraic Number Theory. GTM 84. Springer–Verlag, 1982, 1993. MB: 11471. Rev.: Amer. Math. Monthly 91:5 (1984), 319–321.

[15] N. Jacobson. Basic Algebra I, II. W. H. Freeman, 1980. II, Ch. 9: Valuation Theory; II, Ch. 10: Dedekind Domains.

[16] G. J. Janusz. Algebraic Number Fields. Graduate Studies in Mathematics 7. AMS, ^{2}1995, Jan. 1996. Rekl. in Notices AMS 42:11 (1995), 1370.

[17] H. Koch. Einführung in die klassische Mathematik I. Springer–Verlag, 1986. MB: ?, HB: 1 Bb 1658. Zbl. 652.00001. English Transl.: Kluwer Acad. Publ. 1991.

[18] H. Koch. Algebraic number fields. Encyclopedia of Mathematical Sciences 62. Number Theory II. Springer–Verlag, 1992. MB: 15893 b. Übersicht. Umfangreiches Literaturverzeichnis.

[19] Helmut Koch. Zahlentheorie: Algebraische Zahlen und Funktionen. Vieweg Studium, Aufbaukurs Mathematik. Vieweg, 1997. ISBN 3-528-07272-5. MB:.

[20] S. Lang. Algebraic Numbers. Addison–Wesley Series in Mathematics. Addison–Wesley, 1964. MB: ?

[21] S. Lang. Algebraic Number Theory. Addison–Wesley Series in Mathematics. Addison–Wesley, 1970. MB: ?

[22] S. Lang. Algebraic Number Theory. GTM 110. Springer–Verlag, ^{2}1994. MB: ?

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

[24] F. Lorenz. Algebraische Zahlentheorie. BI, 1993. MB:.

[25] D. Lorenzini. An Invitation to Arithmetic Geometry. Graduate Studies in Mathematics 9. AMS, 1995. MB: . Rekl. in Notices AMS 42:12 (1995), 1574: connections between algebraic number theory and algebraic curves.

[26] D. A. Marcus. Number Fields. Universitext. Springer–Verlag, 1977. MB: 9492. Ch. 4: Galois theory applied to prime decomposition.

[27] Richard A. Mollin. Fundamental Number Theory with Applications. Discrete Mathematics and Its Applications. CRC Press via Springer, 1998. MB: ISBN 0-8493-3987-1.

[28] Richard A. Mollin. Algebraic Number Theory. Discrete Mathematics and Its Applications. CRC Press via Springer, 1999. MB: 18855. ISBN 0-8493-3989-8.

[29] W. Narkiewicz. Elementary and Analytic Theory of Algebraic Numbers. PWN, Warszawa, 1974. MB: ? Zbl. 276.12002.

[30] J. Neukirch. Algebraische Zahlentheorie. Springer–Verlag, 1992. MB: 16296, HB: Bb 1842.

[31] M. Pohst and H. Zassenhaus. Algorithmic Algebraic Number Theory. Encyclopedia of Mathematics and Its Applications. Cambridge Univ. Press, 1989. MB: ?

[32] Michael Pohst, editor. Algorithmic Methods in Algebra and Number Theory, Aus: Journal of Symbolic Computation 4 (1987). Academic Press, 1987. MB: 14442. ISBN 0-12-559190-X.

[33] H. Pollard and H. G. Diamond. The Theory of Algebraic Numbers. MAA, ^{2}1975. MB: ? Elementary parts of classical algebraic number theory.

[34] H. E. Rose. A Course in Number Theory. Clarendon Press, ^{2}1995 paperback. MB: Including briefly the latest work on Fermast’s last theorem.

[35] P. Samuel. Algebraic Theory of Numbers. Kershaw Publ. Co., London, 1972. MB: ? Franz. Original: Théorie algébrique des nombres, Hermann, Paris, 1967.

[36] M. R. Schroeder. Number Theory in Science and Communication. With Applications in Cryptography, Physics, Biology, Digital Information, and Computing. Springer Series in Information Sciences 7. Springer–Verlag, 1984. MB: 12448. Historical Remarks on Fermat’s Last Theorem: 95–96.

[37] H. Schubart. Einführung in die klassische und moderne Zahlentheorie. Unitexte. Vieweg, 1974. MB: 7836.

[38] D. Shanks. Solved and Unsolved Problems in Number Theory. 1962, ^{3}1993. MB:.

[39] I. N. Stewart and D. O. Tall. Algebraic Number Theory. Chapman and Hall Mathematics Series. Chapman and Hall, 1979, ^{2}1987. MB: 10481, HB: Bf7181.

[40] A. Weil. Basic Number Theory. Die Grundlehren der mathematischen Wissenschaften 144; Classics in Mathematics. Springer–Verlag, 1967, 1995. MB: 3867.

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