This award is concerned with the theory of finitedimensional division algebras and the theory of Dubrovin valuation rings. Problems in finite dimensional division algebras will be considered by using valuation theory, both the classical valuation theory of division algebras and the recently developing theory of Dubrovin valuation rings. Specifically, the principal investigator will work on the structure of non-tame division algebras over Henselian valued fields and the structure of defective division algebras. He will also develop a global theory of Dubrovin valuation domains. A ring is an algebraic object having an addition and a multiplication defined on it. Rings occur naturally in many different settings in mathematics. This research is concerned with an important class of rings called division algebras.
