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We give the basic structure of the multivariable Ore extensions S=A[t¯;σ,δ¯] introduced in the work of Martínez-Peñas 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)∈S.
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Leroy et al. (2024) studied this question.
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