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Maximal non-Jaffard subrings of a field
Ben Nasr, Mabrouk
Jarboui, Noôman

Data: 2000
Resum: A domain R is called a maximal non-Jaffard subring of a field L if R [contained in] L, R is not a Jaffard domain and each domain T such that R [contained in] T [contained in] 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 = dimR+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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions matematiques, V. 44 N. 1 (2000) , p. 157-175, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_44100_05
DOI: 10.5565/37979

19 p, 174.3 KB

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