5 papers
The Coproduct of Ideals and the Coprime Spectrum
Frank Murphy-Hernandez, Eduardo Leon-Rodriguez
We introduce the coproduct of ideals and the notion of coprime ideal, extending the Heyting-algebra perspective on ideal lattices to arbitrary commutative rings. The resulting copr…
The Grouplike Functor and Monoidal Adjunctions
Frank Murphy-Hernandez
We construct a categorification of the functor of grouplike elements of a Hopf algebra in the setting of braided monoidal categories. Given a braided bistrong monoidal functor admi…
The Cofree Functor on G-Sets and Its Approximations
Frank Murphy-Hernandez
We study the cofree functor on the category of group actions and examine its categorical and combinatorial properties. Motivated by this construction, we introduce a family of func…
Matricial Closure
Frank Murphy-Hernandez, Francisco Raggi, Jose Rios
We study a closure operator derived from the matrix endofunctor on the category of rings with unity. We investigate the invariance of various ring-theoretic properties under this o…
Classes of Preradicals Induced by Relative Injectivity
Frank Murphy-Hernandez, Jose Ríos
This paper analyzes new classes of preradicals defined as weak forms of left exact and idempotent preradicals. We introduce prehereditary preradicals to generalize the hereditary p…