Attaching topological spaces to a module (I): Sobriety and spatial frames of submodules

In this paper we study some frames associated to an \(R\)-module \(M\). We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of \(Max(M)\). We characterize the soberness of \(Max(M)\) in terms of the point space of that frame. Beside...

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Bibliographic Details
Published in:arXiv.org 2017-05
Main Authors: Mauricio Gabriel Medina Bárcenas, Lorena Morales Callejas, Martha Lizbeth Shaid Sandoval Miranda, Zaldívar, Angel
Format: Article
Language:English
Subjects:
Modules
Topology
Online Access:Get full text
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Summary:In this paper we study some frames associated to an \(R\)-module \(M\). We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of \(Max(M)\). We characterize the soberness of \(Max(M)\) in terms of the point space of that frame. Beside of this, we study the regularity of an spatial frame associated to \(M\) given by annihilator conditions.
ISSN:2331-8422