Scholarlink

In this chapter, we will explore the correspondence between ideals and varieties. In § §1 and 2, we will prove the Nullstellensatz, a celebrated theorem which identifies exactly which ideals correspond to varieties. This will allow us to construct a “dictionary” between geometry and algebra, whereby any statement about varieties can be translated into a statement about ideals (and conversely).

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Algebra–Geometry Dictionary

  • 章节

  • 发表日期：

    2025年

查看全文
  • David A. Cox,
  • John Little,
  • Donal O’Shea

摘要

In this chapter, we will explore the correspondence between ideals and varieties. In § §1 and 2, we will prove the Nullstellensatz, a celebrated theorem which identifies exactly which ideals correspond to varieties. This will allow us to construct a “dictionary” between geometry and algebra, whereby any statement about varieties can be translated into a statement about ideals (and conversely).