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A monogenic Hasse-Arf theorem

James Borger (2004)

Journal de Théorie des Nombres de Bordeaux

I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.

Absolutely S-domains and pseudo-polynomial rings

Noomen Jarboui, Ihsen Yengui (2002)

Colloquium Mathematicae

A domain R is called an absolutely S-domain (for short, AS-domain) if each domain T such that R ⊆ T ⊆ qf(R) is an S-domain. We show that R is an AS-domain if and only if for each valuation overring V of R and each height one prime ideal q of V, the extension R/(q ∩ R) ⊆ V/q is algebraic. A Noetherian domain R is an AS-domain if and only if dim (R) ≤ 1. In Section 2, we study a class of R-subalgebras of R[X] which share many spectral properties with the polynomial ring R[X] and which we call pseudo-polynomial...

Anneaux de Goldman

Jean Guérindon (1969/1970)

Séminaire Dubreil. Algèbre et théorie des nombres

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

Mabrouk Ben Nasr, Ali Jaballah (2023)

Czechoslovak Mathematical Journal

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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