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We present a development of norms and discuss their relationship to factorization. In [10] the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own factorization properties. We discuss in several different environments the relationship between factoring in domains and their respective normsets. We will also discuss the utility of this notion when it comes to multiplicative ideal theory.

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Norms, Normsets, and Factorization

  • 会议论文

  • 发表日期：

    2025年

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  • Jim Coykendall,
  • Richard Hasenauer

摘要

We present a development of norms and discuss their relationship to factorization. In [10] the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own factorization properties. We discuss in several different environments the relationship between factoring in domains and their respective normsets. We will also discuss the utility of this notion when it comes to multiplicative ideal theory.