In abstract algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product RI.
Equivalently, M is torsionless if each non-zero element of M has non-zero image under some R-linear functional f: This notion was introduced by Hyman Bass.
[citation needed] A module is torsionless if and only if the canonical map into its double dual, is injective.
If this map is bijective then the module is called reflexive.
Stephen Chase proved the following characterization of semihereditary rings in connection with torsionless modules: For any ring R, the following conditions are equivalent:[4] (The mixture of left/right adjectives in the statement is not a mistake.)