  We study thick ideals in the stable motivic homotopy category SH(k) and in
its subcategories of compact and of finite cellular objects. If k is a subfield
of the complex or even the real numbers, then using comparison functors we find
thick ideals corresponding to thick ideals in classical or Z/2-equivariant
stable homotopy theory, respectively. We also study motivic Morava K-theories
AK(n), for which we prove the motivic analogue of the decomposition of the
Bousfield class of E(n) into Bousfield classes of K(i)'s over the complex
numbers if p>2. In that case we also prove that AK(n)-acyclicity implies
AK(n-1)-acyclicity.
