Attaching topological spaces to a module (I): Sobriety and spatial frames of submodules
Rings and Algebras
2017-05-11 v4
Abstract
In this paper we study some frames associated to an -module . We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of . We characterize the soberness of in terms of the point space of that frame. Beside of this, we study the regularity of an spatial frame associated to given by annihilator conditions.
Keywords
Cite
@article{arxiv.1612.07407,
title = {Attaching topological spaces to a module (I): Sobriety and spatial frames of submodules},
author = {Mauricio Gabriel Medina Bárcenas and Lorena Morales Callejas and Martha Lizbeth Shaid Sandoval Miranda and Angel Zaldívar},
journal= {arXiv preprint arXiv:1612.07407},
year = {2017}
}
Comments
23 pages, ultimate version with some changes with respect the last version, preliminaries contain more information to give more detail proofs