This award supports research in field theory and commutative algebra. The principal investigator will study the relationship between the multiplicative structure of field extensions which are Galois and certain associated groups and invariants. He will also work on a scheme for computing Picard groups of affine rings over fields that are not necessarily algebraically closed. The computations are heavily influenced by the multiplicative structure of the finite extensions of the base field. A ring is an algebraic object having both an addition and a multiplication defined on it. Every element a in the ring has an additive inverse usually denoted -a. However, elements are not required to have multiplicative inverses. A ring in which every nonzero element has a multiplicative inverse is called a field. This project concerns the relationship between the multiplicative structure of a field and that of its subfields. It involves a combination of techniques from field theory, group theory and number theory.
