Maximal non-Jaffard subrings of a field
- Autores: Mabrouk Ben Nasr, Noôman Jarboui
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 44, Nº 1, 2000, págs. 157-175
- Idioma: inglés
- DOI: 10.5565/publmat_44100_05
- Títulos paralelos:
- Subanillos no-Jaffard máximos de un campo
- Enlaces
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Resumen
A domain R is called a maximal non-Jaffard subring of a field L if $R\subset L$, R is not a Jaffard domain and each domain T such that $R\subset T\subseteq L$ is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying $\dim_v R = \dim R + 1$. 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 R is integrally closed. Moreover, these domains are characterized in terms of the altitude formula in case R is not integrally closed. An example of a maximal non-universally catenarian subring of its quotient field which is not integrally closed is given (Example 4.2). Other results and applications are also given.
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