The research will suppose that R is a commutative two- dimensional Noetherian ring. The primary projects in this proposal are: (1) characterize the partially ordered set of prime ideals for various examples of such rings; and (2) suppose that the ring R has the additional property that there exist only finitely many finitely generated indecomposable R-modules up to local isomorphism. Describe the indecomposable modules of R. This work in commutative algebra and algebraic geometry will examine the lattice structure of the set of prime ideals in the Noetherian ring. The project furthers VPW program objectives to provide opportunities for women to advance their careers in science or engineering through research, and to encourage other women to pursue careers in these areas through the investigator's enhanced visibility as a role model on the host campus. The proposed activities which contribute to the second objective include: short visits by other prominent women mathematicians; meetings with women graduate students in mathematics; teaching courses and participating in seminars.
