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Topology, intersections and flat modules


Authors: Carmelo A. Finocchiaro and Dario Spirito
Journal: Proc. Amer. Math. Soc. 144 (2016), 4125-4133
MSC (2010): Primary 13A15, 13A18, 13C11
DOI: https://doi.org/10.1090/proc/13131
Published electronically: April 25, 2016
MathSciNet review: 3531166
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Carmelo A. Finocchiaro
Affiliation: Dipartimento di Matematica e Fisica, Università degli Studi “Roma Tre”, Largo San Leonardo Murialdo, 1, 00146 Roma, Italy
Address at time of publication: Institute of Analysis and Number Theory, Graz University of Technology, 8010 Graz, Steyrergasse 31/II, Austria
Email: carmelo@mat.uniroma3.it, finocchiaro@math.tugraz.at

Dario Spirito
Affiliation: Dipartimento di Matematica e Fisica, Università degli Studi “Roma Tre”, Largo San Leonardo Murialdo, 1, 00146 Roma, Italy
Email: spirito@mat.uniroma3.it

DOI: https://doi.org/10.1090/proc/13131
Keywords: Zariski topology, overrings, flat ideals.
Received by editor(s): October 1, 2015
Received by editor(s) in revised form: December 10, 2015
Published electronically: April 25, 2016
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society

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