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This chapter contains the main results of Krull’s ideal theory in the language of module and ideal systems. We derive the formalism of spectral module systems in a general frame used for later applications in the theory of higher Prüfer conditions (generalizing semistar invertibility) and for the theory of Nagata and Kronecker function rings.

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Prime and Primary Ideals and Noetherian Conditions

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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 contains the main results of Krull’s ideal theory in the language of module and ideal systems. We derive the formalism of spectral module systems in a general frame used for later applications in the theory of higher Prüfer conditions (generalizing semistar invertibility) and for the theory of Nagata and Kronecker function rings.