# Maximal non-Jaffard subrings of a field.

Mabrouk Ben Nasr; Noôman Jarboui

Publicacions Matemàtiques (2000)

- Volume: 44, Issue: 1, page 157-175
- ISSN: 0214-1493

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topBen 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 -

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