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Weakly compact cardinals and $$\kappa$$-torsionless modules. (English) Zbl 1214.03034
Summary: We prove that every $$\kappa$$-torsionless $$R$$-module $$M$$ of cardinality $$\kappa$$ is torsionless whenever $$\kappa$$ is weakly compact and $$|R|<\kappa$$. We also provide some closure properties for ultraproducts and direct products of $$\kappa$$-torsionless modules. We give an example of a $$\kappa$$-torsionless module that is not torsionless, when $$\kappa$$ is not weakly compact.

##### MSC:
 03E55 Large cardinals 03E75 Applications of set theory 16D80 Other classes of modules and ideals in associative algebras
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