Degree in mathematics, master's degree in mathematical sciences and PhD in mathematical sciences.
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics, Statistics, Probability and Uncertainty, Algebra and Number Theory
4
Scopus Publications
Scopus Publications
ON SEMI-INJECTIVE LATTICES Francisco Gonzalez-bayona, Sebastian Pardo-guerra, Manuel Gerardo Zorrilla-noriega, Hugo Alberto Rincon Mejia International Electronic Journal of Algebra, 2026 In a previous paper, we explored, in the context of the category $ \mathcal{L_M} $ of complete modular lattices and linear morphisms introduced by T. Albu and M. Iosif, the lattice-theoretic counterparts of semi-projective retractable modules and their ring of endomorphisms. In this work, we investigate the dual situation. That is, we introduce the concept of semi-injective coretractable lattices, and we study their relation to their monoid of endomorphisms.
ON SEMI-PROJECTIVE MODULAR LATTICES Francisco Gonzalez Bayona, Sebastian Pardo Guerra, Manuel Gerardo Zorrilla Noriega, Hugo Alberto Rincon Mejia International Electronic Journal of Algebra, 2025 A. Haghany and M. Vedadi, as well as M. K. Patel, explored the relationship between a semi-projective and retractable module and its endomorphism ring. In this work, we study the lattice-theoretic counterparts of these results. To this end, we consider the category of linear modular lattices. Specifically, we show a relation between a retractable and semi-projective complete modular lattice and its monoid of endomorphisms.
On torsion theories and open classes of linear modular lattices Francisco González-Bayona, Sebastián Pardo-Guerra, Hugo Alberto Rincón-Mejía, Manuel Gerardo Zorrilla-Noriega Communications in Algebra, 2024 Given a ring R, a bijection exists between torsion theories and idempotent radicals.Further, the class of hereditary torsion theories contains the skeleton of the open classes.In this work, we extend the notions and main results in R-Mod about torsion classes, torsion-free classes, and open classes to the category L M of linear lattices, whose objects are complete modular lattices and whose morphisms are linear morphisms.
On the lattice of conatural classes of linear modular lattices Sebastián Pardo-Guerra, Hugo A. Rincón-Mejía, Manuel G. Zorrilla-Noriega, Francisco González-Bayona Algebra Universalis, 2023 The collection of all cohereditary classes of modules over a ring R is a pseudocomplemented complete big lattice. The elements of its skeleton are the conatural classes of R-modules. In this paper we extend some results about cohereditary classes in R-Mod to the category $$\mathcal {L_{M}}$$ L M of linear modular lattices, which has as objects all complete modular lattices and as morphisms all linear morphisms. We introduce the big lattice of conatural classes in $$\mathcal {L_{M}}$$ L M , and we obtain some results about it, paralleling the case of R-Mod and arriving at its being boolean. Finally, we prove some closure properties of conatural classes in $$\mathcal {L_{M}}$$ L M .
