Half Condensed Domains

• Autores: D. D. Anderson, Tiberiu Dumitrescu
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 30, Nº 4, 2004, págs. 929-936
• Idioma: inglés
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• Resumen

  • An integral domain D is condensed (resp., strongly condensed) if for each pair of ideals I, J of D, IJ={ij ; i in I, j in J} (resp., IJ=iJ for some i in I or IJ =Ij for some j in J). In this paper we introduce and study the two related notions of a half condensed domain and a strongly half condensed domain. An integral domain D is half condensed if whenever a nonzero z is in IJ with I, J ideals of D, there exist I', J' (invertible) ideals of D such that I' is a subset of I, J' is a subset of J, and zD=I'J'. And D is strongly half condensed if whenever I, J are nonzero ideals of D, IJ=I1J for some invertible ideal I1 that is a subset of I or IJ=IJ1 for some invertible ideal J1 that is a subset of J.