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Displaying similar documents to “A two-dimensional domain whose integral closure is not t-linked.”

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

Noômen Jarboui (2002)

Publicacions Matemàtiques

Similarity:

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).

Maximal non-Jaffard subrings of a field.

Mabrouk Ben Nasr, Noôman Jarboui (2000)

Publicacions Matemàtiques

Similarity:

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...

Absolutely S-domains and pseudo-polynomial rings

Noomen Jarboui, Ihsen Yengui (2002)

Colloquium Mathematicae

Similarity:

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...