CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Condensed and Strongly Condensed Domains

  Published:2008-09-01
 Printed: Sep 2008
  • Abdeslam Mimouni
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

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, 13A15, 13F05, 13E05 show english descriptions Integral domains
Ideals; multiplicative ideal theory
Dedekind, Prufer, Krull and Mori rings and their generalizations
Noetherian rings and modules
13G05 - Integral domains
13A15 - Ideals; multiplicative ideal theory
13F05 - Dedekind, Prufer, Krull and Mori rings and their generalizations
13E05 - Noetherian rings and modules
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/