Abstract
A set of polynomials is called a <em>submodule</em> of $\mathbb C [x_1 ,\ldots , x_n ]$ if it is a translation invariant linear subspace of $\mathbb C [x_1 ,\ldots , x_n ]$. We present a description of the submodules of $\mathbb C [x,y]$ in terms of a
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