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This chapter deals with the classic objects of multiplicative ideal theory: classic and higher (semistar) invertibility and the resulting Prüfer, Dedekind and Krull monoids. While we derive the main characterizations of these structures without cancellation assumptions, we must subsequently restrict to cancellative monoids for the theory of Lorenzen monoids, associated valuation monoids and quasi divisor theories.

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Invertibility, Cancellation and Integrality

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  • 发表日期：

    2025年

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  • Franz Halter-Koch,
  • Alfred Geroldinger,
  • Andreas Reinhart

摘要

This chapter deals with the classic objects of multiplicative ideal theory: classic and higher (semistar) invertibility and the resulting Prüfer, Dedekind and Krull monoids. While we derive the main characterizations of these structures without cancellation assumptions, we must subsequently restrict to cancellative monoids for the theory of Lorenzen monoids, associated valuation monoids and quasi divisor theories.