The principal investigator will conduct research on noncommutative algebras at the University of California, San Diego (September 1 - December 24, 1999), and at the Mathematical Sciences Research Institute in Berkeley, California (January 1 - June 30, 2000), during the program on "Noncommutative Algebra." This research leave will enable her to focus on her existing research problems in noncommutative algebra, with the goal of providing a better understanding of the structure of noncommutative rings. She will continue her work on homological and dimension theoretic questions in noncommutative rings (e.g. the Auslander-Gorenstein condition and the filter dimension), on the properties of down-up algebras and their application to the representation theory of differential partially ordered sets, and on properties of superalgebras. The research leave will also provide her with new methods in noncommutative algebra, particularly in noncommutative algebraic geometry and combinatorial algebraic techniques; she will also learn more about applications to quantum groups and related rings. The ten month research leave will help her become better able to pursue the important questions in noncommutative algebra. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).