VPW: Prime Ideals and Indecomposable Cohen - Macaulay Modules (Algebra)

研究将假设R是可交换的二维Notherian环。这个方案的主要目的是：(1)刻画这类环的各种例子的素数理想的偏序集；(2)设备环R具有附加性质，即直到局部同构只存在有限多个有限生成的不可分解R-模。描述R的不可分解模。这项在交换代数和代数几何中的工作将考察Notherian环中素数理想集的格结构。该项目进一步推动了VPW项目的目标，为女性提供通过研究提升她们在科学或工程领域的职业生涯的机会，并通过调查员作为东道主校园榜样的提高知名度，鼓励其他女性在这些领域追求职业生涯。为第二个目标作出贡献的拟议活动包括：其他杰出女数学家的短期访问；与数学女研究生会面；教授课程和参加研讨会。

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.