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Pseudo linear transformations and evaluation in Ore extensions. (English) Zbl 0840.16023
Author’s summary: The relations between evaluation of Ore polynomials and pseudolinear transformations are studied. The behavior of these transformations under homomorphisms of Ore extensions, in particular with respect to algebraicity, is analyzed leading to characterization of left and right primitivity of an Ore extension.
Necessary and sufficient conditions are given for algebraic pseudolinear transformations to be diagonalizable. Natural notions of \((S,D)\) right and left eigenvalues are introduced and sufficient conditions for a matrix to be \((S,D)\) diagonalizable are given.

16S36 Ordinary and skew polynomial rings and semigroup rings
15A04 Linear transformations, semilinear transformations
15A18 Eigenvalues, singular values, and eigenvectors
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