On some criteria for the balanced projectivity of modules over integral domains
Commutative Algebra
2011-12-06 v1 Group Theory
Abstract
Motivated by Hill's criterion of freeness for abelian groups, we investigate conditions under which unions of ascending chains of balanced-projective modules over integral domains are again balanced-projective. Our main result establishes that, in order for a torsion-free module to be balanced-projective, it is sufficient that it be the union of a countable, ascending chain of balanced-projective, pure submodules. The proof reduces to the completely decomposable case, and it hinges on the existence of suitable families of submodules of the links in the chain. A Shelah-Eklof-type result for the balanced projectivity of modules is proved in the way, and a generalization of Auslander's lemma is obtained as a corollary.
Keywords
Cite
@article{arxiv.1112.0605,
title = {On some criteria for the balanced projectivity of modules over integral domains},
author = {J. E. Macías-Díaz},
journal= {arXiv preprint arXiv:1112.0605},
year = {2011}
}