English

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 RR-module MM. We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of Max(M)Max(M). We characterize the soberness of Max(M)Max(M) in terms of the point space of that frame. Beside of this, we study the regularity of an spatial frame associated to MM 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

R2 v1 2026-06-22T17:31:48.385Z