Right ideals generated by an idempotent of finite rank. (Q734924)

Let \(R\) be a \(K\)-algebra acting densely on \(V(D)\). It is proved that a right ideal \(P\) of \(R\) is generated by an idempotent of finite rank if and only if the rank of \(f(x_1,\dots,x_t)\) is bounded above by the same natural number for all \(x_1,\dots,x_t\in P\). In this case, the rank of the idempotent that generates \(P\) is also explicitly given. The results are then applied to considering the triangularization of \(P\) and the irreducibility of \(f(P)\). Section 2 is proofs and consequences.