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 |
Acceso al artículo completo |