-domains and pseudo-valuations
N. Sankaran, Ram Avtar Yadav (1979)
Rendiconti del Seminario Matematico della Università di Padova
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N. Sankaran, Ram Avtar Yadav (1979)
Rendiconti del Seminario Matematico della Università di Padova
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Dobbs, David E., Fontana, Marco (1991)
International Journal of Mathematics and Mathematical Sciences
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Dobbs, David E. (1985-1986)
Portugaliae mathematica
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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...
Nicolae Popescu, Constantin Vraciu (1985)
Rendiconti del Seminario Matematico della Università di Padova
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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).
Dobbs, David E. (1981)
International Journal of Mathematics and Mathematical Sciences
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Joe L. Mott, M. Zafrullah (1981)
Manuscripta mathematica
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Paolo Valabrega (1974)
Rendiconti del Seminario Matematico della Università di Padova
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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...
Ahmed Ayache, Hanen Monceur (2011)
Colloquium Mathematicae
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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.
Masayoshi Nagata (1974-1975)
Séminaire Dubreil. Algèbre et théorie des nombres
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