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Wikipedia definition
1. Weyl algebraIn abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), More precisely, let F be a field, and let F[X X] be the ring of polynomials in one variable, X, with coefficients in F. Then each fi lies in F[X X]. ∂X is the derivative with respect to X. The algebra is generated by X and ∂X. The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring.
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