Geodesic
Butler Modules Over Valuation Domains
Canadian journal of mathematics, Tome 43 (1991) no. 1, pp. 48-60

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a commutative domain with 1, Q its field of quotients, and M a torsion-free R module. By a balanced submodule of M is meant an RD-submodule N [i.e. rN = N ∩ rM for each r ∈ R] such that, for every R-submodule J of Q, every homomorphism η : J → M/N can be lifted to a homomorphism χ:J → M. This definition extends the notion of balancedness as introduced in abelian groups (see e.g. [10, p. 113]). The balanced-projective R-modules can be characterized as summands of completely decomposable R-modules (i.e. summands of direct sums of submodules of Q). If R is a valuation domain, then such summands are again completely decomposable; see [12, p. 275]. 
Fuchs, L.; Monari-Martinez, E. Butler Modules Over Valuation Domains. Canadian journal of mathematics, Tome 43 (1991) no. 1, pp. 48-60. doi: 10.4153/CJM-1991-004-x
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