# Article

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Keywords:
filtered modules; valuated groups; representations of quivers
Summary:
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.
References:
[1] Beers D., Hunter R., Walker E.A.: Finite valuated $p$-groups. Abelian Group Theory (Honolulu 1983), pp.471-507, Lecture Notes in Mathematics 1006, Springer-Verlag. MR 0722640 | Zbl 0518.20045
[2] Hunter R., Richman F., Walker E.A.: Existence theorems for Warfield groups. Trans. Amer. Math. Soc. 235 (1978), 345-362. MR 0473044 | Zbl 0368.20034
[3] Hunter R., Richman F., Walker E.A.: Subgroups of bounded abelian groups. Abelian Groups and Modules (Udine 1984), pp.17-35, CISM Courses and Lectures 287, Springer-Verlag. MR 0789807 | Zbl 0568.20051
[4] Richman F., Walker E.A.: Valuated groups. J. Algebra 56 (1979), 145-167. MR 0527162 | Zbl 0401.20049

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