Maximal non-Jaffard subrings of a field.

Ben Nasr, Mabrouk, and Jarboui, Noôman. "Maximal non-Jaffard subrings of a field.." Publicacions Matemàtiques 44.1 (2000): 157-175. <http://eudml.org/doc/41387>.

@article{BenNasr2000,
abstract = {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 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.},
author = {Ben Nasr, Mabrouk, Jarboui, Noôman},
journal = {Publicacions Matemàtiques},
keywords = {Anillos conmutativos; Subanillos; Dimensión de Krull; Dominios estructurales; Jaffard ring; valuative dimension; catenarian ring},
language = {eng},
number = {1},
pages = {157-175},
title = {Maximal non-Jaffard subrings of a field.},
url = {http://eudml.org/doc/41387},
volume = {44},
year = {2000},
}

TY - JOUR
AU - Ben Nasr, Mabrouk
AU - Jarboui, Noôman
TI - Maximal non-Jaffard subrings of a field.
JO - Publicacions Matemàtiques
PY - 2000
VL - 44
IS - 1
SP - 157
EP - 175
AB - 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 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.
LA - eng
KW - Anillos conmutativos; Subanillos; Dimensión de Krull; Dominios estructurales; Jaffard ring; valuative dimension; catenarian ring
UR - http://eudml.org/doc/41387
ER -