The space of extended orthomorphisms in a Riesz space

We study the space Orth[infinity](L) of extended orthomorphisms in an Archimedean Riesz space L and its analogies with the complete ring of quotients of a commutative ring with unit element. It is shown that for any uniformly complete f-algebra A with unit element, Orth[infinity](A) is isomorphic with the complete ring of quotients of A. Furthermore, it is proved that for any uniformly complete Riesz space L the space Orth[infinity]( L) is isomorphic to the lateral completion of L. Finally, it is shown that for any uniformly complete Riesz space L the ring Orth[infinity](L) is von Neumann regular.