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Torsion-free and \(\kappa\)-torsion-free modules. (Módulos sin torsión y \(\kappa\)-sin torsión.) (Spanish) Zbl 1120.03023
Aguilar, M. (ed.) et al., 37th national congress of the Mexican Mathematical Society, Ensenada, Mexico, October 10–15, 2004. Proceedings. México: Sociedad Matemática Mexicana. Aportaciones Matemáticas. Comunicaciones 35, 251-264 (2005).
Summary: We present a number of characterizations of torsion-free modules as well as their main properties. Then, we study some classes of rings closely related to torsion-free modules. Moreover, we describe \(\kappa\)-torsion-free modules and prove, under certain cardinal restrictions and assuming the existence of a strongly compact cardinal, that all \(\kappa\)-torsion-free modules are torsion-free.
For the entire collection see [Zbl 1111.00007].
MSC:
03C55 Set-theoretic model theory
03C60 Model-theoretic algebra
16B70 Applications of logic in associative algebras
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
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