Torsionless module

In abstract algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product R^I. Equivalently, M is torsionless if each non-zero element of M has non-zero image under some R-linear functional f:

${\displaystyle f\in M^{\ast }=\operatorname {Hom} _{R}(M,R),\quad f(m)\neq 0.}$

This notion was introduced by Hyman Bass.^{[citation needed]}