Geodesic
Smooth invariants and $\omega$-graded modules over $k[X]$
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 445-448.

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It is shown that every $\omega$-graded module over $k[X]$ is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian $p$-groups.
Classification : 13F20, 16G20, 16W50, 20K10
Keywords: filtered modules; valuated groups; representations of quivers 
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     title = {Smooth invariants and $\omega$-graded modules over $k[X]$},
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Richman, Fred. Smooth invariants and $\omega$-graded modules over $k[X]$. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 445-448. http://geodesic.mathdoc.fr/item/CMUC_2000__41_3_a1/