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Algebraic geometry studies solutions of polynomial equations by building a dictionary between the geometry of the solution sets and the algebra of the defining polynomial equations. In this preliminary chapter, we develop the algebraic notions of polynomial rings that are prerequisite to the study of algebraic geometry. The chapter culminates with a proof of the important fact that every polynomial over a field factors uniquely into irreducible polynomials.

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Polynomial Rings

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Emily Clader,
  • Dustin Ross

摘要

Algebraic geometry studies solutions of polynomial equations by building a dictionary between the geometry of the solution sets and the algebra of the defining polynomial equations. In this preliminary chapter, we develop the algebraic notions of polynomial rings that are prerequisite to the study of algebraic geometry. The chapter culminates with a proof of the important fact that every polynomial over a field factors uniquely into irreducible polynomials.