Mathematical Sciences: Verbally Prime Algebras

This project is concerned with the study of verbally prime p.i. algebras. These algebras are basic building blocks in the theory of T-ideals. The principal investigator will study the structure of generic models, embedding theorems, and applications of invariant theory. This research is in the general area of noncommutative ring theory. In particular, it is concerned with a class of rings which satisfy a polynomial equation. This area, with the discovery of combinatorial theorems that provide insight into the structure theory of the algebra, has become an exciting topic of current research in ring theory with implications for representation theory.