Mathematical Sciences: Division Algebras and Valuation Theory

这个奖项是关于理论的， 有限维可除代数与Dubrovin理论 估值环 有限维除法中的问题 代数将被认为是通过使用赋值理论， 除代数的经典赋值理论和 最近发展的Dubrovin赋值环理论。 具体来说，首席研究员将致力于 Hensel值上非驯服除代数结构 域和亏除代数的结构。 他 还将发展Dubrovin估值的全球理论 域. 一个环是一个代数对象有一个加法和一个 乘法定义。环自然出现在许多 不同的数学环境。 这项研究关注 一类重要的环叫做除代数。

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.