Open AccessTopology, intersections and flat modules
Author(s) -
Carmelo Antonio Finocchiaro,
Dario Spirito
Publication year - 2016
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/13131
Subject(s) - annotation , conjecture , type (biology) , semantics (computer science) , intersection (aeronautics) , algorithm , ideal (ethics) , computer science , linear subspace , mathematics , discrete mathematics , artificial intelligence , pure mathematics , programming language , ecology , philosophy , epistemology , engineering , biology , aerospace engineering
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