2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71584We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional expectations onto the subalgebras.17 pages, to appear in International Journal of MathematicsOperator AlgebrasMathematical PhysicsIntersections of finite families of finite index subfactorstext