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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.

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