A locally convex cone is called linear over R (resp. C) if the scalar
multiplication is extended to all real (resp. complex) numbers and a w
eakened version of the distributive law holds. We show that every loca
lly convex cone may be embedded into a cone that is linear over R (res
p. C). We investigate continuous linear Functionals on these cones and
introduce a new (modular) topology. (C) 1997 Academic Press.