On questions related to saturated chains of primes in polynomial rings |
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Authors: | Ihsen Yengui |
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Institution: | Department of Mathematics, Faculty of Sciences, 3018 Sfax, Tunisia |
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Abstract: | We propose to give positive answers to the open questions: is R(X,Y) strong S when R(X) is strong S? is R stably strong S (resp., universally catenary) when RX] is strong S (resp., catenary)? in case R is obtained by a (T,I,D) construction. The importance of these results is due to the fact that this type of ring is the principal source of counterexamples. Moreover, we give an answer to the open questions: is R〈X1,…,Xn〉 residually Jaffard (resp., totally Jaffard) when R(X1,…,Xn) is ? We construct a three-dimensional local ring R such that R(X1,…,Xn) is totally Jaffard (and hence, residually Jaffard) whereas R〈X1,…,Xn〉 is not residually Jaffard (and hence, not totally Jaffard). |
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Keywords: | 13A15 13B25 13C15 |
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