9 papers
The Burnside ring of simple -sets
José Miguel Calderón León, Alberto G. Raggi-Cárdenas, Itzel Rosas +1
The Burnside ring of a finite category, introduced by Webb, generalizes the classical Burnside ring of a finite group. However, unlike the classical case, the Burnside ring of a fi…
A note on simple actions of small monoids
Ramón H. Ruiz-Medina
These notes aim to exemplify the concept of action and partial action of a finite monoid , identifying among the so-called indecomposable actions those that are also simple. We…
Finite generating sets for monoids of -equivariant functions
Ramón H. Ruiz-Medina, Victor M. Lara-Gómez, Gerardo Romero-Rosales
Given the action of a group on a set , the set of all -equivariant functions, i.e., those satisfying for all and , forms a mono…
Characterization of groupoid categories in terms of its category of -sets
J. Miguel Calderón, Alberto Gerardo Raggi-Cárdenas, Itzel Rosas +1
A -set is a functor from the category to the category of finite sets and functions. The category of -sets, $\mathcal{C} - \operatorname*{set…
Green relations over finite monoids of -equivariant functions
Ramon H- Ruiz-Medina, Victor M. Lara-Gómez
For a group acting over a set , the set of all the -equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\…
Cardinalities in finite monoids of -equivariant functions
Ramón H. Ruiz-Medina
A set with a group action is referred to as a -set, and the set of functions that commute with this action forms a monoid under function composition. This paper examines the cas…
El monoide de endomorfismos de -conjuntos: estructuras y otras propiedades algebraicas
Ramón H. Ruiz-Medina
Given the action of a group on a set , an endomorphism of is a function which is -equivariant, that is, it commutes with the action, i.e., $f(g\cd…
Special cases on the relative rank of G-equivariant functions over an infinite G-set
Ramón H Ruiz-Medina
Given the action of a group on a set , the set of -equivariant functions, those that commute with the action, i.e., for all $ x \in…
The relative rank of the endomorphism monoid of a finite -set
Alonso Castillo-Ramirez, Ramón H. Ruiz-Medina
For a group acting on a set , let be the monoid of all -equivariant transformations, or -endomorphisms, of , and let be its grou…