Announcements

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About Myself.

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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 (2011-2016) 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 Vilchis-Montalvo. At BUAP I taught two undergraduate and two graduate courses, and I supervised a graduate thesis. From August 2021 to July 2023, I 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, rings and modules for undergraduated students. After that, from August 2023 to November 2024, I worked 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. After that, I spent 6 months at Universidad de Guadalajara in the state of Jalisco in México working in rings, modules and lattices with Prof. Angel Zaldívar Corichi. Nowadays, I visiting assistant professor at Universidad Autónoma Metropolitana in Mexico City. 

My research interests

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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. I like how techniques from the pointfree topology can be taken to modules and rings, and how many situations in modules have a natural set-up in certain lattices (idioms). 


Research Statement