Nido V., Juan A.; Mendoza I., Pablo; Villegas S., Luis M. Weakly compact cardinals and \(\kappa\)-torsionless modules. (English) Zbl 1214.03034 Rev. Colomb. Mat. 43, No. 2, 139-164 (2009). 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. Cited in 1 Document MSC: 03E55 Large cardinals 03E75 Applications of set theory 16D80 Other classes of modules and ideals in associative algebras Keywords:torsionless module; \(\kappa\)-torsionless module; weakly compact cardinal PDFBibTeX XMLCite \textit{J. A. Nido V.} et al., Rev. Colomb. Mat. 43, No. 2, 139--164 (2009; Zbl 1214.03034) Full Text: EuDML EMIS