Topology, intersections and flat modules | Zendy

Carmelo A. Finocchiaro | Zendy; Dario Spirito | Zendy

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Topology, intersections and flat modules

Author(s) -

Carmelo A. 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

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