This award supports work on the representation theory of finite dimensional algebras. The principal investigator intends to investigate certain classes of representations from a structure-theoretic point of view. This will require a closer understanding of the geometry of families of uniserial modules and modules with uniserial building blocks. The principal investigator will also explore contravariant finiteness of subcategories of categories of finitely generated modules and, in particular, will develop concrete criteria for the presence of this finiteness property. She will also examine contravariantly finite closures of a given modules category obtained by passing through a sequence of one-point extensions of the underlying algebra. 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 in 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.
