Algebraic Number Theory and Commutative Algebra

Catalog description

This course is an introduction to algebraic number theory and related aspects of commutative algebra. The main objects of study are algebraic number fields, finite extensions of the rational numbers, and their rings of integers. The course will cover topics in ideal theory, Dedekind domains, integral elements, units and unit groups, class groups, valuations, and local-global principles. Applications such as to Diophantine equations will be included as appropriate. Additional topics may be introduced at the instructor's discretion.