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

Noômen Jarboui

Displaying similar documents to “When is each proper overring of R an S(Eidenberg)-domain?”

Maximal non-Jaffard subrings of a field.

Mabrouk Ben Nasr, Noôman Jarboui (2000)

Publicacions Matemàtiques

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A domain R is called a maximal non-Jaffard subring of a field L if R ⊂ L, R is not a Jaffard domain and each domain T such that R ⊂ T ⊆ L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim R = dim R + 1. Further characterizations are given. Maximal non-universally catenarian subrings of their quotient fields are also studied. It is proved that this class of domains coincides with the previous class when...

Fragmented integral domains

Dobbs, David E. (1985-1986)

Portugaliae mathematica

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A two-dimensional domain whose integral closure is not t-linked.

Dumitrescu, Tiberiu (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On locally divided integral domains and CPI-overrings.

Dobbs, David E. (1981)

International Journal of Mathematics and Mathematical Sciences

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On a lifting problem for principal Dedekind domains

Paolo Valabrega (1974)

Rendiconti del Seminario Matematico della Università di Padova

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Absolutely S-domains and pseudo-polynomial rings

Noomen Jarboui, Ihsen Yengui (2002)

Colloquium Mathematicae

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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...

Universally catenarian domains of D $+$ M type. II.

Dobbs, David E., Fontana, Marco (1991)

International Journal of Mathematics and Mathematical Sciences

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On some results of L. J. Ratliff

M. Brodmann (1978)

Compositio Mathematica

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Intermediate domains between a domain and some intersection of its localizations

Mabrouk Ben Nasr, Noômen Jarboui (2002)

Bollettino dell'Unione Matematica Italiana

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In this paper, we deal with the study of intermediate domains between a domain $R$ and a domain $T$ such that $T$ is an intersection of localizations of $R$ , namely the pair $(R, T)$ . More precisely, we study the pair $(R, R_{d})$ and the pair $(R, \tilde{R})$ , where $R_{d} = \cap \{R_{M} ∣ M \in Max (R), h t M = dim R\}$ and $\tilde{R} = \cap \{R_{M} ∣ M \in Max (R), h t M \geq 2\}$ . We prove that, if $R$ is a Jaffard domain, then $(R, R_{d} [n])$ is a Jaffard pair, which generalize [5, Théorème 1.9]. We also show that if $R$ is an $S$ -domain, then $(R, \tilde{R})$ is a residually algebraic pair (that is for each intermediate domain $S$ between $R$ and $\tilde{R}$ , if $Q$ is a prime...