Article
MSC:
13B02,
13B22,
13B30,
13E15,
13E99,
13F05,
13G05 | MR 4632865 | Zbl 07729545 | DOI: 10.21136/CMJ.2023.0358-22
Full entry | Fulltext not available
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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
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
Summary:
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.
References:
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