NOTES ON THE KERNELS OF LOCALLY FINITE HIGHER DERIVATIONS IN POLYNOMIAL RINGS

摘要

Let A = k([3]) be the polynomial ring in three variables over a field k, and let D be a nontrivial locally finite iterative higher derivation on A. Let A(D) denote the kernel of D. In this note, we prove that, if char k > 0 and ML(A(D)) not equal A(D), then A(D) congruent to k([2]). As a consequence of this result, we give another proof of the cancellation theorem for k([2]) over any field k of positive characteristic.