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

本研究假设R是一个可交换的二维诺瑟环。本文的主要工作是：(1)刻画了这类环的各种实例的偏序素理想集；(2)假设环R具有只存在有限多个有限生成的不可分解R模直至局部同构的附加性质。本文在交换代数和代数几何中研究了诺瑟环中素理想集合的晶格结构。该项目进一步推进了VPW项目的目标，即通过研究为女性提供在科学或工程领域发展的机会，并通过研究者在主办校园中作为榜样的知名度提高，鼓励其他女性在这些领域追求职业。促进第二个目标的拟议活动包括：其他杰出女数学家的短期访问；会见数学专业的女研究生；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.