Affine algebraic geometry in dimensions two and three

二维和三维仿射代数几何

• 批准号: RGPIN-2015-04539
• 负责人: Daigle, Daniel
• 金额: $ 1.02万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589861
• 关键词: Affine; algebraic; geometry; dimensions; two

In Algebra, a set of objects that can be added and multiplied is called a "ring". For instance, consider the set of all polynomials in the three variables x,y,z. This is a set of objects (the objects being the polynomials), and these objects can be added and multiplied (we learn in highschool how to add and multiply two polynomials), so this set of polynomials is an example of a ring; it is called the ring of polynomials in three variables, and I shall denote it by R[3]. Similarly, if n is any positive integer, one can consider the ring of polynomials in n variables, which I denote by R[n].

在代数中，一组可以相加和相乘的对象被称为“环”。 例如，考虑三个变量x，y，z的所有多项式的集合。 这是一组对象（对象是多项式），这些对象可以相加和相乘（我们在高中学习如何相加和相乘两个多项式），所以这组多项式是环的一个例子;它被称为三元多项式环，我将用R表示它。 类似地，如果n是任何正整数，可以考虑n个变量的多项式环，我用R[n]表示。