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Condensed and Strongly Condensed Domains

Published online by Cambridge University Press:  20 November 2018

Abdeslam Mimouni
Abdeslam Mimouni*
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. e-mail: [email protected]
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Abstract

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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 $a\,\in \,I\,or\,I\,J\,=\,Ib$ 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.

Keywords

13G0513A1513F0513E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 3 , 01 September 2008 , pp. 406 - 412
Copyright
Copyright © Canadian Mathematical Society 2008

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