  We prove the following: Let (M,g,X) be a noncompact four dimensional
shrinking soliton with bounded nonnegative curvature operator, then (M,g) is
isometric to R^4 or a finite quotient of S^2xR^2 or S^3xR. In the process we
also show that a complete shrinking soliton (M,g,X) with bounded curvature is
gradient and k-noncollapsed and the dilation of a Type I singularity is a
shrinking soliton. Further in dimension three we show shrinking solitons with
bounded curvature can be classified under only the assumption of Rc>= 0.
