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Equations for the set of overrings of normal rings and related ring extensions

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Abstract

We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.

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Acknowledgements

The author extends his thanks to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, 3018, Sfax, BP 802, Tunisia

    Mabrouk Ben Nasr

  2. College of Sciences, Department of Mathematics, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    Ali Jaballah

Authors
  1. Mabrouk Ben Nasr
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  2. Ali Jaballah
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Corresponding author

Correspondence to Ali Jaballah.

Additional information

The author would like to thank University of Sharjah for Funding the Research Project No. 1902144081.

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Nasr, M.B., Jaballah, A. Equations for the set of overrings of normal rings and related ring extensions. Czech Math J 73, 921–935 (2023). https://doi.org/10.21136/CMJ.2023.0358-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0358-22

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