Question

Let V =(infinite direct sum)eik where k is a field. For any n, let Sn be the set of endomorphisms λ ∈ E = End(Vk) such that λ stabilizes (sum over i=1,n)eik and λ(ei) = 0 for i ≥ n + 1. For any i, j, let Eij ∈ E be the linear transformation which sends ej to ei and all ej' to zero. Show that any k-subalgebra R of E containing all the Eij ’s is dense in E and hence left primitive.