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

Thick ideals in equivariant and motivic stable homotopy categories