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Condensed and Strongly Condensed Domains

Published:2008-09-01
Printed: Sep 2008
• Abdeslam Mimouni
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Abstract

This paper deals with the concepts of condensed and strongly condensed domains. By definition, an integral domain $R$ is condensed (resp. strongly condensed) if each pair of ideals $I$ and $J$ of $R$, $IJ=\{ab/a \in I, b \in J\}$ (resp. $IJ=aJ$ for some $a \in I$ or $IJ=Ib$ for some $b \in J$). More precisely, we investigate the ideal theory of condensed and strongly condensed domains in Noetherian-like settings, especially Mori and strong Mori domains and the transfer of these concepts to pullbacks.
 MSC Classifications: 13G05 - Integral domains 13A15 - Ideals; multiplicative ideal theory 13F05 - Dedekind, Prufer, Krull and Mori rings and their generalizations 13E05 - Noetherian rings and modules