arXiv subjects

Mauricio Gabriel Medina Bárcenas

Publications and source records attributed to Mauricio Gabriel Medina Bárcenas.

2 recordsLinked to original sources

arXiv2020

On the de Morgan's laws for modules

In this investigation, we give a module-theoretic counterpart of the well known Demorgan's laws for rings and topological spaces. We observed that the corresponding like Demorgan's laws on a module holds precisely when the module has a certain kind of structure. Besides the considerations of Demorgan's laws for ordered structures (idiomatic-quantales) the manuscript goes back to the ring theoretic realm, in this case, we study the non-commutative counterpart of Dedekind domains this consideration leads to the concept of Asano prime ring.

math.RA↗

arXiv2017

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 of this, we study the regularity of an spatial frame associated to $M$ given by annihilator conditions.

math.RA↗