The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings

Gil Alon, Angelot Behajaina, Elad Paran

We study zeros of polynomials in the multivariate skew polynomial ring $D[x_1,\dots ,x_n;\sigma ]$, where $\sigma$ is an automorphism of a division ring $D$. We prove a generalization of Nog…