Mathematical Sciences: Non-Commutative Ring Theory

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This project is concerned with various areas of noncommutative ring theory. The principal investigator will study PI rings and their representations focusing on applications to linear groups, the behavior of normalizing elements and the embeddability of PI rings into matrices. Affine prime rings with Gelfand-Kirillov dimension two will also be investigated with the goal of determining when they are primitive. Finally, rings of invariants of reductive groups on certain noncommutative algebras will be considered. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.