Announcements
My paper "\(\mathfrak{m}\)Baer and \(\mathfrak{m}\)Rickart lattices" in collaboration
with Prof. Hugo RincónMejía has been publish in the journal Order.
My contact information has changed, see at the bottom of the page.
with Prof. Hugo RincónMejía has been publish in the journal Order.
My contact information has changed, see at the bottom of the page.
About Myself.
I was born in Mexico city in 1987. I became a mathematician in 2010 and I got my Ph.D. in Sep. 2016 from Universidad Nacional Autónoma de México (UNAM), with my dissertation "Some generalizations of ring theory in Wisbauer categories" under the supervision of Prof. José Ríos Montes. During my master and Ph.D. at UNAM (20112016) I was instructor at Facultad de Ciencias (UNAM) where I taught different topics in algebra. After that, I was postdoc at Chungnam National University from Jan 2017 to Jun 2018. There, I worked with Prof. Gangyong Lee on generalizations of (semi)hereditary rings. From Sep 2018 to June2019 I was a Fulbright Scholar at Northern Illinois University. Here, I was working with Prof. John A. Beachy on the universal localization at a semiprime Goldie Ideal and in generalizations of fully prime and semiprime rings in categories of type Sigma[M]. Later, I was posdoct at Benemérita Universidad Autónoma de Puebla(BUAP) from August 2019 to July 2021 working with Dr. Fernando VilchisMontalvo. In BUAP I taught two undergraduate and two graduate courses, and I supervised a graduate thesis. From August 2021 to July 2023, I am worked with Prof. Hugo Rincón Mejía at Facultad de Ciencias (UNAM) as posdoc. We wrote two papers in which the concepts of Rickart, Baer and Endoregular modules are taken to lattices using linear morphisms. In this position I taught algebra courses in the subjects of group theory, Galois theory and rings and modules for undergraduated students. Nowadays, I am working in an engineering project studying some possible applications of lattices and categories at Centro de Ingeniería y Desarrollo Industrial (CIDESI), located in the city of Querétaro in Mexico.

My research interests
My research focuses on noncommutative rings and their modules as well as their relation with ordered structures. I am interested in those generalizations of rings in the moduletheoretic context, principally those related with Goldie rings and (semi)prime rings. I am also interested in the characterizations of modules using their endomorphism rings. I like the relationships between ordered structures and modules and rings such as frames and quantales. Nowadays, I have been working with the notion of Rickart and Baer modules in complete modular lattices. Also, I am working in the concept of singularity and torsion theoretic aspects in sets of intervals of a complete modular lattice, in collaboration with Prof. Lizbeth Sandoval Miranda and Prof. Angel Zaldivar Corichi.
I am learning and finding general properties of the universal localization of a ring at a semiprime Goldie ideal. In 2018, I worked with my colleges on Boyle's Conjecture which states that every left QIring is left hereditary. We approached it using perfect torsion theories but we were unable to prove it or deny it. Also, when I was visiting Hacettepe University in 2016, Ç. Özcan and I, in our paper "Primitive submodules, Cosemisimple and Regular modules", found that it is not known if a prime left Vring is left nonsingular (a statement considered true). So, it would be very nice to know something new about Boyle's Conjecture and the nonsingularity of prime Vrings.
My projects (some for now, some for later) are on:
Research Statement
I am learning and finding general properties of the universal localization of a ring at a semiprime Goldie ideal. In 2018, I worked with my colleges on Boyle's Conjecture which states that every left QIring is left hereditary. We approached it using perfect torsion theories but we were unable to prove it or deny it. Also, when I was visiting Hacettepe University in 2016, Ç. Özcan and I, in our paper "Primitive submodules, Cosemisimple and Regular modules", found that it is not known if a prime left Vring is left nonsingular (a statement considered true). So, it would be very nice to know something new about Boyle's Conjecture and the nonsingularity of prime Vrings.
My projects (some for now, some for later) are on:
 The approach of Baer and Rickart modules using lattice theory.
 Moduletheoretic concepts from the point of view of sets of intervals and operators in complete modular lattices.
 Characterizations of those modules which their lattice of submodules is a quantale.
 Properties of Goldie rings in the context of categories of type \(\sigma[M]\)
 Finding a moduletheoretic analogue of quasiduo rings.
 Studying the general structure of the universal localization at a semiprime Goldie ideal.
 Boyle's conjecture.
 Prime Vrings.
Research Statement