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When studying the integers, a key tool is the existence of prime factorizations. There is an analogue when studying polynomials (factorization into irreducibles) or when studying finite abelian groups (decomposition as a direct sum of cyclic groups). These settings all demonstrate the way in which one can understand a class of mathematical objects by specifying the atomic, indecomposable objects as well as how a general object decomposes into its atomic pieces.

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Irreducibility of Affine Varieties

  • 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

When studying the integers, a key tool is the existence of prime factorizations. There is an analogue when studying polynomials (factorization into irreducibles) or when studying finite abelian groups (decomposition as a direct sum of cyclic groups). These settings all demonstrate the way in which one can understand a class of mathematical objects by specifying the atomic, indecomposable objects as well as how a general object decomposes into its atomic pieces.