  We investigate homogeneity in the special Colombeau algebra. It is shown that
strongly scaling invariant functions on the d-dimensional space are simply the
constants. On the pierced space, strongly homogeneous functions admit tempered
representatives, whereas on the whole space, such functions are polynomials
with generalized coefficients. We also introduce weak notions of homogeneity
and show that these are consistent with the classical notion on the
distributional level. Moreover, we investigate the relation between generalized
solutions of the Euler differential equation and homogeneity.
