Summary: In this paper we consider classes of vector lattices over subfields of the real numbers. Among other properties we relate the archimedean condition of such a vector lattice to the uniqueness of scalar multiplication and the linearity of \(\ell\)-automorphisms. If a vector lattice in the classes considered admits an essential subgroup that is not a minimal prime, then it also admits a nonlinear \(\ell\)-automorphism and more than one scalar multiplication. It is also shown that each \(\ell\)-group contains a largest archimedean convex \(\ell\)-subgroup which admits a unique scalar multiplication.