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In recent work Goebel and Goldsmith investigated the spectrum of maximal pure subgroups of certain Abelian groups. Here the situation relating to maximal pure submodules of a torsion-free module over an integral domain R is investigated. Connections to the level of coherency are established along with a detailed investigation of the situation where all maximal pure submodules are isomorphic to a product of copies of the ring R.
Goldsmith, B., Zenardo, P.:On Maximal Relatively Divisible Submodules. Houston Journal of Mathematics, Forthcoming.