ALGEBRAIC NUMBER THEORY

Code: MA509 | L-T-P-C: 3-0-0-6

Algebraic numbers, transcendental numbers, minimal polynomial, conjugates. Number fields, primitive element, real and complex embeddings, norm, trace and discriminant. Algebraic integers, ring of integers in a number field, integral basis. Dedekind domain, ideal factorization, fractional ideal, ideal class group. Lattices, Minkowski's theory, computation of class group of number fields. Dirichlet Unit Theorem, fundamental units, units in quadratic fields, Pell's equation. Cyclotomic fields.

Texts:

1. Richard A. Mollin, Algebraic Number Theory, CRC Press, 1999.
2. J. Neukirch, Algebraic Number Theory, Springer, 1999.
3. Stewart and Tall, Algebraic Number Theory and Fermat's Last Theorem, A K Peters, 2002.

References:

1. Alan Baker, A Concise Introduction to Algebraic Number Theory,Cambridge University Press,1994.
2. Janusz G.J., Algebraic Number Fields, GSM, vol-7, AMS, 1996.
3. Marcus, D. A., Number Fields, Springer, 1977.