Topology, intersections and flat modules

Finocchiaro, Carmelo; Spirito, Dario

doi:10.1090/proc/13131

Topology, intersections and flat modules
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by Carmelo A. Finocchiaro and Dario Spirito PDF

Proc. Amer. Math. Soc. 144 (2016), 4125-4133 Request permission

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.

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