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This chapter contains the basics of the calculus of module systems. Beyond the notions which are familiar from the theory of ideal systems (and are presented now without cancellation assumptions), we give a first introduction to Marot conditions, we develop the theory of v- and t-ideals in a general setting, and we investigate Manis valuations from an ideal-theoretic point of view.

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The Formalism of Module and Ideal Systems

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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 basics of the calculus of module systems. Beyond the notions which are familiar from the theory of ideal systems (and are presented now without cancellation assumptions), we give a first introduction to Marot conditions, we develop the theory of v- and t-ideals in a general setting, and we investigate Manis valuations from an ideal-theoretic point of view.