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.
Original language | English |
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Pages (from-to) | 4125 - 4133 |
Journal | Proceedings of the American Mathematical Society |
Volume | 144 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2016 |