On universally catenarian pairs |
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Authors: | Mohamed Jaouhar Ben Abdallah |
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Institution: | Faculty of Sciences of Sfax, Department of Mathematics, 3018 Sfax, P.O. Box: 802, Tunisia |
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Abstract: | If 1≤n<∞ and R⊆S are integral domains, then (R,S) is called an n-catenarian pair if for each intermediate ring T (that is each ring T such that R⊆T⊆S) the polynomial ring in n indeterminates, Tn] is catenarian. This implies that (R,S) is m-catenarian for all m<n. The main purpose of this paper is to prove that 1-catenarian and universally catenarian pairs are equivalent in several cases. An example of a 1-catenarian pair which is not 2-catenarian is given. |
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Keywords: | Primary 13B02 secondary 13C15 13A17 13A18 13B25 13E05 |
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