Abstract
In this paper, we give some results on closed polynomials and factorially closed polynomials in n variables which are generalizations of results in [7], [12] and [13]. In particular, we give a characterization of factorially closed polynomials in n variables over an algebraically closed field of any characteristic. Furthermore, as an application of results on closed polynomials, we determine kernels of non-zero monomial derivations on the polynomial ring in two variables over a UFD. Finally, by using this result and the argument in [16, §5], for a field k, we determine the non-zero monomial derivations D on k[x,y] such that the quotient field of the kernel of D is not equal to the kernel of D in k(x,y).
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