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ABSTRACT
Theorems in the theory of polynomial mappings which are true over fields are considered for nonreduced rings: counterexamples are given, and some generalisations are made. Equivalence of the cancellation problem over a ring with the cancellation problem over the ring modulo its nilradical is proved. For polynomial maps satisfying
it is shown that there is equivalence between 1) F is linearisable by conjugation; 2)
is linearisable by conjugation, where
is F modulo the nilradical of R.