Displaying similar documents to “Absolutely S-domains and pseudo-polynomial rings”

When is each proper overring of R an S(Eidenberg)-domain?

Noômen Jarboui (2002)

Publicacions Matemàtiques

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A domain R is called a maximal "non-S" subring of a field L if R ⊂ L, R is not an S-domain and each domain T such that R ⊂ T ⊆ L is an S-domain. We show that maximal "non-S" subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim(R) = 1, dim(R) = 2 and L = qf(R).

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

Mabrouk Ben Nasr, Ali Jaballah (2023)

Czechoslovak Mathematical Journal

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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.

Essential Cover and Closure

Andruszkiewicz, R. (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05. We construct some new examples showing that Heyman and Roos construction of the essential closure in the class of associative rings can terminate at any finite or the first infinite ordinal.