Let G be a group, Ω a set and K = {g ∈ G | ω * g = ω, Ɐω ∈ Ω} the nucleus of Ω where G acts on the set Ω. We will show that G/K is simple in the case that the group G verifies to be primitive on Ω, as well as that it is equal to its derived subgroup and finally if α ∈ Ω then Gα has a subgroup A that is abelian and normal such that G =< Ag | g ∈ G >, where Gα is the stabilizer of α in G. To finish we will give an application that the alternating group A5 is simple.

Plantea mejorar el teorema Max Noether a través de la construcción de la compactación, donde el espacio de modulo original se ve como un abrir en un espacio más grande, permitiendo que las curvas admitan singularidades, siempre que éstas sean Gorenstein

Expone lo que son las categorías y funtores para luego demostrar el teorema de Yoneda con su corolario más importante, que es la inmersión de Yoneda, luego definiremos el funtor de puntos de esquemas y gracias a la inmersi´on de Yoneda daremos una definición alternativa de esquema, tal vez la más natural sobre la óptica geométrica.

In this work, we will prove Cayley theorem, using category theory. We will see a different proof than the one seen in a Group Theory course, in this case we will use a famous result in category theory called the Yoneda lemma and then, to relate groups with such lemma we will take advantage of the fact that every group can be viewed as a category. This proof shows that Yoneda lemma is an extensive generalization of Cayley theorem for groups.

In this work, we will prove the Cayley-Hamilton theorem using algebraic geometry. We will see a different proof than the one seen in a linear algebra course, in this case we will use the Zariski topology, then we will take advantage of the fact that every square matrix of order n _ n, with entries in a field K, denoted by (aij)n_n can be seen as an element of the affine space of dimension n _ n over the field K and thanks to this, we can resort to algebraic sets and algebraic varieties in order to obtain some results seen in an algebraic geometry and to get a proof of the Cayley-Hamilton theorem.

We are going to characterize the natural isomorphism between the bifunctors of the examples 2.13 and 2.14, for that it is enough to show that η and ζ of the lemma 3.1 are natural isomorphisms.

In this work we establishe relations between modules over a ring and vector spaces, we show results of linear algebra that can be extended to modules and we present counterexamples to those ones that cannot be extended. By identify abelian groups with Z-modules we classify every the finitely generated abelian groups and we show a decomposition in direct sum of ciclic subgroups. Finally, we apply the results about finitely generated abelian groups to determine the rational canonical form of an endomorphis of finitely generated K[t]-modules and simplify the computer of associated numbers to the endomorphism, for example: therank and the determinant.

Una de las ciencias más significativas de poder abstraer el mundo donde vivimos es la matemática; y con las matemáticas se puede construir modelos. Los modelos matemáticos permiten analizar y proyectar la dinámica del fenómeno que estamos estudiando. En este sentido, la ecología matemática ha aportado enormemente al estudio de la dinámica de las especies, y esta importancia es vital para los estudiantes de ciencias de la vida. La modelización computacional enseña de manera dinámica y didáctica la construcción de propuestas para luego estudiarlas de manera matemática. Este proceso permite complementar un análisis matemático y una construcción informática donde el estudiante aborda, desde la creatividad diferentes formas de modelar un problema ecológico que puede extenderlo a la epidemiología de una manera intuitiva, pero con fundamento científico para poder seguir ab...