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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. 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]. Nowadays, I am posdoct at Benemérita Universidad Autónoma de Puebla(BUAP) working with Dr. Fernando Vilchis-Montalvo. During my master and Ph.D. at UNAM (2011-2016) I was instructor at Facultad de Ciencias (UNAM) where I taught different topics in algebra.
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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 module-theoretic 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 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 QI-ring 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, Co-semisimple and Regular modules", found that it is not known if a prime left V-ring 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 V-rings.
My projects (some for now, some for later) are on:
My projects (some for now, some for later) are on:
- Generalizing (semi)hereditary rings using Rickart modules.
- Finding a module-theoretic analogue of quasi-duo rings.
- Studying the general structure of the universal localization at a semiprime Goldie ideal.
- The algebraic de Morgan laws in modules.
- Boyle's conjecture.
- Prime V-rings.