When is an N-ring Noetherian?
A ring (resp. domain) R is called an N-ring (domain) if for each ideal I in R there is a Noetherian ring (domain) T, \(\supseteq R\), such that \(IT\cap R=I\). These concepts were introduced by \textit{R. Gilmer} and \textit{W. Heinzer} [J. Pure Appl. Algebra 24, 123-144 (1982; Zbl 0495.13002)]. Substantial comment is made on these and related ring conditions (Laskerian, Mori, etc.). The question of the title leads the authors to obtain conditions for an intersection of 1-dimensional local Noetherian domains to be Noetherian. Highlight of the paper is perhaps the development of an example by Hochster, cited by the authors in J. Pure Appl. Algebra 32, 115-127 (1984; see the preceding review), to obtain a 1-dimensional quasilocal domain which is an N-ring but not an N-domain.
scientific article; zbMATH DE number 3922818
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