Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Characteristic and minimal polynomial of an element relative to a
finite extension, Equivalent definitions of norm and trace, Algebraic
numbers, algebraic integers and their properties.
- Integral bases, discriminant, Stickelberger's theorem, Brille's
theorem, description of integral basis of quadratic, cyclotomic and
special cubic fields.
- Ideals in the ring of algebraic integers and their norm, factorization
of ideals into prime ideals, generalised Fermat's theorem and Euler's
theorem.
- Dirichlet's theorem on units, regulator of an algebraic number fields,
explicit computation of fundamental units in real quadratic fields.
- Dedekind's theorem for decomposion of rational primes in algebraic
number fields and its application, splitting of rational primes in
quadratic and cyclotomic fields.
- Saban Alaca and Kenneth Williams, Introductory Algebraic Number
Theory, Cambridge University Press (2003).
- M. Ram Murty and J. Esmonde Problems in Algebraic Numbers
Theory, Springer-Verlag (2004).
- Wladyslaw Narkiewicz, Elementary and Analytic Theory of
Algebraic Numbers, Springer-Verlag (2004).
- Erich Hecke, Lectures on the Theory of Algebraic Numbers,
Springer-Verlag (1981).
- Paula Ribenboim, Algebraic Numbers, John Wiley & Sons (1972).
- Harry Pollard and Harold Diamond, The Theory of Algebraic
Numbers, Dover Publications (2010).
