Abstract
Yuqun Chen and K. P. Shum in [Rees short exact sequence of S-systems, Semigroup Forum 65 (2002), 141–148] introduced Rees short exact sequence of acts and considered conditions under which a Rees short exact sequence of acts is left and right split, respectively. To our knowledge, conditions under which the induced sequences by functors Hom(RLS, –), Hom(–, RLS) and AS ⊗ S– (where R, S are monoids) are exact, are unknown. This article addresses these conditions. Results are different from that of modules.