THE LINEARISATION CONJECTURE AND OTHER PROBLEMS OVER NONREDUCED RINGS

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.

Acknowledgments