1 | Learns the structure of the rings and homomorphisms and studies the examples. |
2 | Can set up the structures of ideals and division rings. |
3 | Learns the Rings of Power Series. |
4 | Define the Product at Polynomial Rings. |
5 | Knows the definitions of Modules, Vector Spaces, Projective and Injective Modules, Hom and Duality, Tensor Product, Algebras and prove the theorems. |
6 | Can express and prove the theorems of Field Extensions, Splitting Fields, Algebraic Closure and Normality, Galaois Group of Polinomials, Finite Fields, Separability, Transcendence Bases, Linear Disjointness and Separability. |