Geodesic
On Chain Conditions in Integral Domains
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 351-359

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The following two theorems are proved. If R is an Archimedean conducive integral domain, then R is quasilocal and dim(R) ≤1. If each overring of an integral domain R has ascending chain condition on divisorial ideals, then the integral closure of R is a Dedekind domain. Both theorems sharpen results already known in the Noetherian case. The second theorem leads to a strengthened converse of the Krull-Akizuki Theorem. We also investigate the effect of restricting the hypothesis in the second theorem to the proper overrings of R.
DOI : 10.4153/CMB-1984-053-1
Mots-clés : 13E05, 13F05, 13B20, 13G05 
Barucci, Valentina; Dobbs, David E. On Chain Conditions in Integral Domains. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 351-359. doi: 10.4153/CMB-1984-053-1
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     title = {On {Chain} {Conditions} in {Integral} {Domains}},
     journal = {Canadian mathematical bulletin},
     pages = {351--359},
     year = {1984},
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     number = {3},
     doi = {10.4153/CMB-1984-053-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-053-1/}
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