It is well known that, in general, multiplication by an ideal I does not commute with the intersection of a family of ideals, but that this fact holds if I is flat and the family is finite. We generalize this result by showing that finite families of ideals can be replaced by compact subspaces of a natural topological space, and that ideals can be replaced by submodules of an epimorphic extension of a base ring. As a particular case, we give a new proof of a conjecture by Glaz and Vasconcelos.

Topology, intersections and flat modules

Spirito D.
2016

Abstract

It is well known that, in general, multiplication by an ideal I does not commute with the intersection of a family of ideals, but that this fact holds if I is flat and the family is finite. We generalize this result by showing that finite families of ideals can be replaced by compact subspaces of a natural topological space, and that ideals can be replaced by submodules of an epimorphic extension of a base ring. As a particular case, we give a new proof of a conjecture by Glaz and Vasconcelos.
File in questo prodotto:
File Dimensione Formato  
finocchiaro-spirito-revision.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 307.66 kB
Formato Adobe PDF
307.66 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1215710
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact