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The converse to a well known theorem on Noetherian rings. (English) Zbl 0155.07903

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[1] Cohen, I. S.: Commutative rings with restricted minimum condition. Duke Math. J.17, 27-42 (1950). · Zbl 0041.36408 · doi:10.1215/S0012-7094-50-01704-2
[2] Gilmer, Jr., R. W.: Contracted ideals with respect to integral extensions. (To appear in Duke Math. J.)
[3] Jacobson, N.: Lectures in abstract algebra, Vol. III. Princeton: D. Van. Nostrand Company 1964. · Zbl 0124.27002
[4] Nagata, M.: Local Rings. New York: Interscience 1962. · Zbl 0123.03402
[5] Zariski, O., and P. Samuel: Commutative algebra, Vol. 1. Princeton: 1958. · Zbl 0081.26501
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