Mathematical Sciences: Polynomial Identities and Graded Identities

New machinery has recently been introduced into the study of PI algebras which show that the study of Z/2Z-graded algebras yields information about the identities of PI algebras. This project is concerned with investigating these algebras, especially their graded identities. This research is in the general area of noncommutative ring theory. In particular, it is concerned with a particular 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 and the symmetric group.