Abstract
This note is devoted to the study of divisible modules over arbitrary commutative domains R with 1. Whereas divisible modules over Dedekind domains can be completely characterized by numerical invariants, not much is known about their structures in the general case. Divisible modules have been studied by Matlis [6] who was the first to distinguish between divisibility in general and h-divisibility. He established an important duality between h-divisible torsion modules and complete torsion-free R-modules [7] . Matlis [6] and Hamsher [4] characterized those domains R for which all divisible R-modules are h-divisible, e.g. by the property that the field Q of quotients of R has projective dimension 1.
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References
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© 1984 Springer-Verlag Wien
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Fuchs, L. (1984). On divisible modules over domains. In: Göbel, R., Metelli, C., Orsatti, A., Salce, L. (eds) Abelian Groups and Modules. International Centre for Mechanical Sciences, vol 287. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2814-5_25
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DOI: https://doi.org/10.1007/978-3-7091-2814-5_25
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81847-3
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