  A new simple model exhibiting a noise-induced ordering transition (NIOT) and
a noise-induced disordering transition (NIDT), in which the noise is purely
multiplicative, is presented. Both transitions are found in two as well as in
one dimension (where they had not been previously reported). We show
analytically and numerically that the critical behavior of these two
transitions is described by the so called multiplicative noise(MN) universality
class. A computation of the set of critical exponents is presented in both
$d=1$, and $d=2$ (where they have not been previously measured).
