Maximal non-Jaffard subrings of a field.

Título inglés Maximal non-Jaffard subrings of a field.
Título español Subanillos no-Jaffard máximos de un campo.
Autor/es Ben Nasr, Mabrouk ; Jarboui, Noôman
Organización Dep. Math. Fac. Sci. Univ. Sfax, Sfax, Túnez
Revista 0214-1493
Publicación 2000, 44 (1): 157-175, 22 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés A domain R is called a maximal non-Jaffard subring of a field L if R Ì L, R is not a Jaffard domain and each domain T such that R Ì T Í L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dimv 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.
Clasificación UNESCO 120105
Palabras clave español Anillos conmutativos ; Subanillos ; Dimensión de Krull ; Dominios estructurales
Código MathReviews MR1775744
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