Abstract
We study the rings of nilpotent elements of R-derivations D on polynomial rings over a UFD R containing . The main result of this paper determines of the monomial derivations D on . Furthermore, as its application, we prove that, for each positive integer m, there exists a monomial R-derivation with a slice on such that the minimal number of generators of its kernel equals m.
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2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to thank Professors Shigeru Kuroda and Takanori Nagamine for their helpful comments on this research.