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Retracts that are kernels of locally nilpotent derivations

Dayan LiuXiaosong Sun — 2022

Czechoslovak Mathematical Journal

Let k be a field of characteristic zero and B a k -domain. Let R be a retract of B being the kernel of a locally nilpotent derivation of B . We show that if B = R I for some principal ideal I (in particular, if B is a UFD), then B = R [ 1 ] , i.e., B is a polynomial algebra over R in one variable. It is natural to ask that, if a retract R of a k -UFD B is the kernel of two commuting locally nilpotent derivations of B , then does it follow that B R [ 2 ] ? We give a negative answer to this question. The interest in retracts comes...

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