On a categorical version of a generalized projectivity criterion for modules over domains
DOI:
https://doi.org/10.33064/iycuaa2011534495Keywords:
Module categories, ascending chains of modules, torsion-free modules, Hill’s Criterion, pure submodules, integral domainsAbstract
In this work, we establish a generalization of Hill's Criterion of freeness of abelian group theory, to categories M of torsion-free modules over integral domains, which are closed with respect to the formation of direct sums, and in which every member can be decomposed into direct sums of modules of M of rank at most a fix limit cardinal number K. Our main result states that a module belongs to M if it is the union of a continuous, well-ordered, ascending chain of length k, consisting of pure submodules which belong in.
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Copyright (c) 2011 Jorge Eduardo Macías Díaz
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