Studies In Commutative Algebra & Algebraic Geometry

交换代数研究

• 批准号: 9401428
• 负责人: Melvin Hochster
• 金额: $ 58.48万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401428&HistoricalAwards=false
• 关键词: Studies; Commutative; Algebra; & Algebraic

9401428 Hochster This award supports research in commutative algebra and algebraic geometry. The principle investigator will continue investigating several long standing questions in the theory of Noetherian rings, to explore the relationship of these questions with the burgeoning theory of tight closure, including its relationship to absolute integral closures and to achieve a better understanding of the geometric significance of the condition on a ring that all of its ideals be tightly closed. The faculty associate will study primary decompositions of ideals, tight closure, mixed multiplicities, joint reductions and ideals generated by monomials in a system of parameters in a local ring. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry. ***

小行星9401428 该奖项支持交换代数和代数几何的研究。 主要调查员将继续调查几个长期存在的问题在理论的诺特环，探讨这些问题的关系与新兴理论的紧封闭，包括其关系的绝对积分封闭和实现更好地理解的几何意义的条件环，其所有的理想是紧密封闭的。 教师助理将研究主要分解的理想，紧封闭，混合多重性，联合减少和理想所产生的单项式在一个系统的参数在一个本地环。 本研究涉及交换代数和代数几何中的一些问题。 代数几何研究多项式方程族的解。 人们既可以研究解集的几何，也可以通过研究形成交换环的解集上的某些函数来代数地处理问题。 这种双重视角在交换代数和代数几何之间建立了密切的联系。***