Abstract: It is known that every completely j-simple semigroup is isomorphic to a normalized Rees matrix semigroup
over a ? - monoid. Utilizing this result, we show that the homomorphism of a completely j-simple
semigroup is a good homomorphism. Consequently, we give a construction theorem of homomorphisms
between completely j-simple semigroups. This result strengthens the one given by Ren et al. (2018) on
homomorphisms of completely j-simple semigroups
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