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.
@article{urn:eudml:doc:41387,
title = {Maximal non-Jaffard subrings of a field.},
journal = {Publicacions Matem\`atiques},
volume = {44},
year = {2000},
pages = {157-175},
mrnumber = {MR1775744},
zbl = {0976.13007},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41387}
}
Ben Nasr, Mabrouk; Jarboui, Noôman. Maximal non-Jaffard subrings of a field.. Publicacions Matemàtiques, Tome 44 (2000) pp. 157-175. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41387/