On some criteria for the balanced projectivity of modules over integral domains

zbMATH Open1229.13012arXiv1112.0605MaRDI QIDQ3108409

Jorge Eduardo Macías-Díaz

Publication date: 3 January 2012

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.

Full work available at URL: https://arxiv.org/abs/1112.0605

zbMATH Keywords

pure submodulesintegral domainsdirect limitscomplete decomposabilityascending chains of modules

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Projective and free modules and ideals in commutative rings (13C10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (2)

Balanced projectives and axiom 3 ⋮ CHAINS OF PROJECTIVE MODULES

This page was built for publication: On some criteria for the balanced projectivity of modules over integral domains

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3108409)