9 papers
On non-archimedean frames
Francisco Ávila, Miriam Bocardo-Gaspar, Julio Urenda +1
In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these fram…
On the Cantor and Hilbert Cube Frames and the Alexandroff-Hausdorff Theorem
Francisco Ávila, Julio Urenda, Angel Zaldívar
The aim of this work is to give a pointfree description of the Cantor set. It can be shown that the Cantor set is homeomorphic to the -adic integers $\mathbb{Z}_{p}:=\{x\in\math…
The Frame of Nuclei of an Alexandroff Space
Francisco Ávila, Guram Bezhanishvili, Patrick Morandi +1
Let be the frame of open sets of a topological space , and let be the frame of nuclei of . For an Alexandroff space , we prove…
When is the frame of nuclei spatial: A new approach
Francisco Ávila, Guram Bezhanishvili, Patrick Morandi +1
For a frame , let be the Esakia space of . We identify a special subset of consisting of nuclear points of , and prove the following results: is sp…
Attaching topological spaces to a module (I): Sobriety and spatial frames of submodules
Mauricio Gabriel Medina Bárcenas, Lorena Morales Callejas, Martha Lizbeth Shaid Sandoval Miranda +1
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 to…
Boyle's Conjecture and perfect localizations
Jaime Castro Pérez, Mauricio Medina Bárcenas, José Ríos Montes +1
In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle's c…
On some operators and dimensions in modular meet-continuous lattices
Mauricio Medina Bárcenas, José Ríos Montes, Angel Zaldívar
Given a complete modular meet-continuous lattice , an inflator on is a monotone function such that for all . If is the se…
A generalization of quantales with applications to modules and rings
Mauricio Medina Bárcenas, Angel Zaldívar, Martha Lizbeth Shaid Sandoval Miranda
We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R…
A Note on Gabriel dimension for idioms
Angel Zaldívar
The aim of this note is to illustrate that the definition and construction of the Gabriel dimension for modular lattices in the classical sense is the same as the module case follo…