Question

If the ring $End_{k}(V)$ is a simple ring, the prove that V is finite dimensional vector space over the field k.

Answer 1

Answer:

Step-by-step explanation:

Let V be a finite-dimensional vector space over a field F. Let W be a subspace of V .... Proof. Since V is finite dimensional, and N(T) ⊆ V is a subspace, N(T) is finite dimensional ... sides of this equation, and recalling that vi ∈ N(T) for all i ∈ {1,...,k}, we get ..... β takes a rather simple form, and therefore T becomes easier.

Answer 2

Answer:

Step-by-step explanation:

Let V be a finite-dimensional vector space over a field F. Let W be a subspace of V .... Proof. Since V is finite dimensional, and N(T) ⊆ V is a subspace, N(T) is finite dimensional ... sides of this equation, and recalling that vi ∈ N(T) for all i ∈ {1,...,k}, we get ..... β takes a rather simple form, and therefore T becomes easier.