Homomorphisms of completely J -simple semigroups
It is known that every completely J -simple semigroup is isomorphic to a normalized Rees
matrix semigroups over a cancellative monoid. By using this result, we prove that the homomorphism of
a completely J -simple semigroup is a good homomorphism. Consequently, a method of construction of
such a homomorphism is described in this paper. Some necessary and sucient conditions for a completely
J -simple semigroups to be an isomorphism are given.