A decomposition theorem for neutrices

Neutrices are convex additive subgroups of the nonstandard space R^k, most of them are external sets. Because of the convexity and the invariance under some translations and multiplications, external neutrices are models for orders of magnitude. One dimensional neutrices have been applied to asymptotics, singular perturbations, and statistics. This paper shows that in R^k, with standard k, every neutrix is the direct sum of k neutrices of R. These components may be chosen to be orthogonal.