Introduction to the
Theory of Algebraic Numbers
Math 722

Fall Semester, 2001

August 29, 2001

Course Outline

  1. Valued Fields and Valuation Rings

  2. Dedekind Domains and Rings of Algebraic Integers

  3. Unique Factorization, Divisors, and Ideals

  4. Unit Group

  5. Class Group

  6. Adeles and Ideles

REFERENCES

[1]   Emil Artin, Theory of Algebraic Numbers, multigraphed notes by G. Würges based on lectures at Göttingen, 1956-57, translated to English 1959 and distributed by G. Striker, Schildweg 12, Göttingen.

[2]   Z. I. Borevich & I. R. Shafarevitch, Number Theory, Academic Press, 1966.

[3]   J. W. S. Cassels & A. Fröhlich, eds., Algebraic Number Theory, conference proceedings, Thompson Book Co., Washington, D. C., 1967.

[4]   Martin Eichler, Einführung in die Theorie der algebraischen Zahlen und Funktionen, Birkhäuser, 1963.

[5]   A. Fröhlich & M. J. Taylor, Algebraic Number Theory, Cambridge University Press, 1991.

[6]   Erich Hecke, Vorlesungen über die Theorie der Algebraischen Zahlen, U. S. reprint, Chelsea Publishing Co., New York, 1948.

[7]   Serge Lang, Algebraic Number Theory, Addison-Wesley, 1970.

[8]   André Weil, Basic Number Theory, Springer-Verlag, 1967.

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