Mathematical Sciences: Representation Theory of Artin Algebras

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This research is concerned with the representation theory of artin algebras. The principal investigator will study idempotent ideals and other generalizations of quasihereditary algebras and their usefulness in the reduction of problems to algebras with fewer simple modules. She will also study contravariantly finite subcategories of finitely generated modules over artin algebras with regard to the finitestic global dimension conjecture and existence of almost split sequences. This research is in the general area of ring theory. A ring is an algebraic structure having both an addition and a multiplication defined on it. These objects arise naturally and are important in many areas of mathematics and physics.