Top local cohomology modules over local rings and the weak going-up property

• Asghar Farokhi ^[1] ; Alireza Nazari ^[1]
  1. [1] Lorestan University

     Lorestan University

     Irán

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 1, 2019, págs. 209-215
• Idioma: inglés
• DOI: 10.33044/revuma.v60n1a12
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• Resumen

  • Let (R,m) be a Noetherian local ring and let ˆR denote the m-adic completion of R. In this paper, we introduce the concept of the weak going-up property for the extension R⊆ˆR and we give some characterizations of this property. In particular, we show that this property is equivalent to the strong form of the Lichtenbaum–Hartshorne Vanishing Theorem. Also, when R satisfies the weak going-up property, we show that for a finitely generated R-module M of dimension d, and ideals a and b of R, we have AttR(Hda(M))=AttR(Hdb(M)) if and only if da(M)≅Hd(M), and we find a criterion for the cofiniteness of Artinian top local cohomology modules.