Condensed and Strongly Condensed Domains

Abstract

AbstractThis 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, I J = ﹛ab/a ∈ I, b ∈ J﹜ (resp. I J = a J for some a ∈ I or I J = 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.