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| Home > Articles > Published articles > Maximal non-Jaffard subrings of a field |
| Date: | 2000 |
| Abstract: | 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. |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Published in: | Publicacions matemàtiques, V. 44 N. 1 (2000) , p. 157-175, ISSN 2014-4350 |
