Abstract
Let k be a field of characteristic zero. This paper studies a problem proposed by Joseph F. Ritt in 1950. Precisely, we prove that(1)If p⩾2 is an integer, for every integer i∈N, the nilpotency index of the image of Ti in the ring k{T}/[Tp] equals (i+1)p−i.(2)For every pair of integers (i,j), the nilpotency index of the image of TiUj in the ring k{T}/[TU] equals i+j+1.
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