Geodesic
Equations for the set of overrings of normal rings and related ring extensions
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 921-935.

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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.
DOI : 10.21136/CMJ.2023.0358-22
Classification : 13B02, 13B22, 13B30, 13E15, 13E99, 13F05, 13G05
Keywords: total ring of fractions; ring extension; intermediate ring; overring; finite direct product; FIP extension; FCP extension; integrally closed; integral domain; Prüfer domain; valuation domain; normal pair; normal ring; length of ring extension; number of intermediate ring; number of overring 
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     title = {Equations for the set of overrings of normal rings and related ring extensions},
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Ben Nasr, Mabrouk; Jaballah, Ali. Equations for the set of overrings of normal rings and related ring extensions. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 921-935. doi : 10.21136/CMJ.2023.0358-22. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0358-22/

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