Abstract For a division ring the polynomials can be evaluated “on the left” and “on the right” giving rise to left and right Lagrange interpolation problems. The problems containing interpolation conditions of the same type were considered in [7] where the solvability criterion was given in terms of polynomial independence of interpolation nodes. We establish the solvability criterion and describe all solutions of low degree (less than the number of interpolation conditions imposed) for the problem containing both “left” and “right” conditions.

中文翻译：

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除法环上的拉格朗日插值

摘要 对于除法环，多项式可以在“左侧”和“右侧”求值，从而产生左右拉格朗日插值问题。在[7]中考虑了包含相同类型插值条件的问题，其中根据插值节点的多项式独立性给出了可解性标准。我们建立了可解性标准并描述了包含“左”和“右”条件的问题的所有低度（小于所施加的插值条件的数量）的解决方案。