  We introduce the notion of torsion-simple objects in an abelian category:
these are the objects which are always either torsion or torsion-free with
respect to any torsion pair. We present some general results concerning their
properties, and then proceed to investigate the notion in various contexts,
such as the category of modules over an artin algebra or a commutative
noetherian ring, and the category of quasi-coherent sheaves over the projective
line.
