Classification of split torsion torsionfree triples in module categories

A TTF-triple (C,T,F)(C,T,F) in an abelian category is one-sided split   in case either (C,T)(C,T) or (T,F)(T,F) is a split torsion theory. In this paper we classify one-sided split TTF-triples in module categories, thus completing Jans’ classification of two-sided split TTF-triples and answering a question that has remained open for almost 40 years.