Abstract
In this paper, we study closed polynomials of the polynomial ring in n variables over an integral domain. By using the techniques on \(\mathbb {Z}\)-gradings on the polynomial ring, we give some sufficient conditions for a polynomial f to be a closed polynomial. We also give a correspondence between closed polynomials and derivations in the polynomial ring R[x, y] in two variables over a UFD R containing \(\mathbb {Q}\).
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Nagamine, T. (2020). On Some Sufficient Conditions for Polynomials to Be Closed Polynomials over Domains. In: Kuroda, S., Onoda, N., Freudenburg, G. (eds) Polynomial Rings and Affine Algebraic Geometry. PRAAG 2018. Springer Proceedings in Mathematics & Statistics, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-030-42136-6_10
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DOI: https://doi.org/10.1007/978-3-030-42136-6_10
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