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.
Finocchiaro, C.A., Spirito, D. (2016). Topology, intersections and flat modules. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 144(10), 4125-4133 [10.1090/proc/13131].
Topology, intersections and flat modules
Finocchiaro, Carmelo A.;Spirito, Dario
2016-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
