Some remarks on the inverse systems of polynomial modules (Q1295542)

Let \(R=K[x_1,x_2, \dots,x_n]\) be the ring of polynomials over a field \(K\), \(I\) be an ideal of \(R\). Macaulay's inverse system [\textit{F. S. Macaulay}, ``The algebraic theory of modular systems'' (Cambridge 1916; JFM 46.0167.01)] can be considered as an \(R\)-submodule \(H\) in \(\Hom_K(R,K)\) such that \(\text{Ann} H=I\). The author generalizes this notion for the case of an \(A\)-submodule of \(A^{\ell}\), where \(A\) is an associative algebra over \(K\) with unit element. In the case \(A=R\), a finite system of generators for an inverse system is indicated with the help of the Janet theory [\textit{M. Janet}, J. Math. Pure Appl. (8) 3, 65-151 (1920; JFM 47.0440.03) and ``Leçons sur les systèmes d'équations aux dérivées partielles'' (Paris 1929; JFM 55.0276.01)].