WHEN DOES THE RING K[Y] HAVE THE COEFFICIENT ASSIGNMENT PROPERTY

If K is an algebraically closed field, then it is known that K[y] has the coefficient assignment property. Conversely, suppose that the fiel d K has characteristic zero and contains the primitive nth roots of un ity for all positive integers n. If K[y] has the coefficient assignmen t property, then K is closed under taking nth roots for all positive i ntegers n.