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1. Torsion Free Module

   Linked via "rational extension"

   Relation to Rational Extensions
   Torsion-free modules are intimately connected to the concept of rational extension. A module $M$ over an integral domain $R$ is torsion-free if and only if the canonical inclusion map $\iota: M \to M \otimes_R Q$ is an isomorphism, where $Q$ is the field of fractions of $R$. This mirrors the property of vector spaces over a field, suggesting that torsion-free modules are the "closest algebraic analogues to vector spaces" when the base ring…