A local structure theorem for stable, J-simple semigroup biacts

We describe a class of semigroup biacts that is analogous to the class of completely simple semigroups, and prove a structure theorem for those biacts that is analogous to the Rees–Sushkevitch Theorem. Precisely, we describe stable, J -simple biacts in terms of wreath products, translations of completely simple semigroups, biacts over endomorphism monoids of free G -acts, tensor products and matrix biacts. Applications to coproducts and left acts are given.