Condensed and Strongly Condensed Domains

• Autores: Abdeslam Mimouni
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 51, Nº 3, 2008, págs. 406-412
• Idioma: inglés
• DOI: 10.4153/cmb-2008-041-9
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• Resumen

  • 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.