Geodesic
Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras
Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 111-114

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DOI

If R is a Dedekind domain, then div splits i.e.; the maximal divisible submodule of every R-module M is a direct summand of M. We investigate the status of this result for some finite-dimensional hereditary algebras. We use a torsion theory which permits the existence of torsion-free divisible modules for such algebras. Using this torsion theory we prove that the algebras obtained from extended Coxeter- Dynkin diagrams are the only such hereditary algebras for which div splits. The field of rational functions plays an essential role. The paper concludes with a new type of infinite-dimensional indecomposable module over a finite-dimensional wild hereditary algebra.
DOI : 10.4153/CMB-1996-014-9
Mots-clés : 16D70, 16G60, 13C12 
Okoh, F. Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras. Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 111-114. doi: 10.4153/CMB-1996-014-9
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     year = {1996},
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     doi = {10.4153/CMB-1996-014-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-014-9/}
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