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arXiv · 2602.19342

Structure and arithmetic of multivariate Ore extensions

André Leroy·Huda Merdach
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Abstract

We give the basic structure of the multivariable Ore extensions $S=A[\underline{t} ; \sigma, \underline{\delta}]$ introduced in the work of Mart\'inez-Pe\~nas and Kschischang. The Pseudo multilinear transformations (PMT's) are introduced and correspond to modules over $S$. These maps are strongly connected to the evaluation of polynomials in $S$. A general product formula is obtained. PMT's help to put some structure on the set of roots of a polynomial $f(t) \in S$.

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André Leroy, Huda Merdach. 2026-02-22. Structure and arithmetic of multivariate Ore extensions. https://doi.org/10.1080/00927872.2024.2387049

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