  Tensor products usually have nonzero torsion. This is a central theme of
Auslander's paper "Modules over unramified regular local rings"; the theme
continues in the work of Huneke and Wiegand. The main focus in this note is on
tensor powers of a finitely generated module over a local ring. Also, we study
torsion-free modules N with the property that its tensor product with any
module M has torsion, unless M is very special. Important examples of such
modules N are the Frobenius power of a ring, viewed as a module over itself,
that is a complete intersection domain of positive characteristic.
