Condensed and strongly condensed domains

Abdeslam Mimouni

doi:10.4153/CMB-2008-041-9

Condensed and strongly condensed domains

Abdeslam Mimouni^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 ∈ I, b ∈ J} (resp. IJ = aJ for some a ∈ I or IJ = Ib for some b ∈ 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.

Original language	English
Pages (from-to)	406-412
Number of pages	7
Journal	Canadian Mathematical Bulletin
Volume	51
Issue number	3
DOIs	https://doi.org/10.4153/CMB-2008-041-9
State	Published - Sep 2008

ASJC Scopus subject areas

General Mathematics

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title = "Condensed and strongly condensed domains",

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 ∈ I, b ∈ J\} (resp. IJ = aJ for some a ∈ I or IJ = Ib for some b ∈ 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.",

author = "Abdeslam Mimouni",

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N2 - 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 ∈ I, b ∈ J} (resp. IJ = aJ for some a ∈ I or IJ = Ib for some b ∈ 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.

AB - 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 ∈ I, b ∈ J} (resp. IJ = aJ for some a ∈ I or IJ = Ib for some b ∈ 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.

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DO - 10.4153/CMB-2008-041-9

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JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

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Condensed and strongly condensed domains

Abstract

ASJC Scopus subject areas

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