Abstract
The diagonal right act of a semigroup S is the set S × S, with S acting by componentwise multiplication from the right. The diagonal left act and diagonal bi-act of S are defined analogously.
Necessary and sufficient conditions are found for the finite generation of the diagonal bi-acts of completely zero-simple semigroups and completely simple semigroups. It is also proved that various classes of semigroups do not have finitely generated or cyclic diagonal right, left, or bi-acts.
Notes
Communicated by V. Gould.