In this seminar, you'll learn how various concepts of the integers, for example the prime factorisation, can be generalised to finite field extensions of the rational numbers. For this manner, the more robust theory of Dedekind rings is worked out and combined with Galois theory.

The course explores the arithmetic of and connection between sums of two, respectively four, squares and the Gaussian integers, respectively the integral quaternions. Multiplication laws for sums of two and four squares arise and we answer the question for which other numbers such laws may exist. Finally, the arithmetic and multiplicative structure of binary quadratic forms are explored.