Mathematical Sciences: Division Algebras and Valuation Theory

该奖项涉及有限维除代数理论和Dubrovin赋值环理论。有限维除代数中的问题将用赋值理论来考虑，赋值理论既有经典的除代数赋值理论，也有新近发展起来的Dubrovin赋值环理论。具体地说，主要的研究人员将致力于Henselian值域上的非驯服除法代数的结构和亏除代数的结构。他还将提出杜布罗文估值领域的全球理论。环是定义了加法和乘法的代数对象。在数学中，环在许多不同的环境中自然出现。这项研究涉及一类重要的环，称为除法代数。

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.