# Smooth invariants and $\omega $-graded modules over $k\left[X\right]$

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 3, page 445-448
- ISSN: 0010-2628

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topRichman, Fred. "Smooth invariants and $\omega $-graded modules over $k[X]$." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 445-448. <http://eudml.org/doc/248623>.

@article{Richman2000,

abstract = {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.},

author = {Richman, Fred},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {filtered modules; valuated groups; representations of quivers; filtered modules; valuated Abelian -groups; representations of quivers; smooth invariants; graded modules},

language = {eng},

number = {3},

pages = {445-448},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Smooth invariants and $\omega $-graded modules over $k[X]$},

url = {http://eudml.org/doc/248623},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Richman, Fred

TI - Smooth invariants and $\omega $-graded modules over $k[X]$

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 3

SP - 445

EP - 448

AB - 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.

LA - eng

KW - filtered modules; valuated groups; representations of quivers; filtered modules; valuated Abelian -groups; representations of quivers; smooth invariants; graded modules

UR - http://eudml.org/doc/248623

ER -

## References

top- 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. Zbl0518.20045MR0722640
- Hunter R., Richman F., Walker E.A., Existence theorems for Warfield groups, Trans. Amer. Math. Soc. 235 (1978), 345-362. (1978) Zbl0368.20034MR0473044
- 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. Zbl0568.20051MR0789807
- Richman F., Walker E.A., Valuated groups, J. Algebra 56 (1979), 145-167. (1979) Zbl0401.20049MR0527162

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