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

研究假设R是一个可交换的二- 维Noether环 本建议书中的主要项目 （1）刻画了素理想的偏序集 这类环的各种例子;（2）假设环R 有一个额外的属性，即只存在 到局部R-模的非生成不可分解R-模 同构 描述R的不可分解模。 这项工作在交换代数和代数几何 将检查的格结构的一套素理想中， 诺特环 该项目进一步推动了VPW计划的目标， 妇女在科学领域发展事业的机会， 通过研究工程，并鼓励其他妇女， 追求职业生涯在这些领域通过调查员的增强 作为东道校园的榜样。 拟议 有助于实现第二个目标的活动包括： 其他著名女数学家的访问;与 数学专业的女研究生;教学课程和 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.