GREEN ♯-RELATIONS AND NORMAL ${\cal H}^\sharp$-CRYPTOGROUPS
Xiangzhi Kong, K. P. Shum · Asian-European Journal of Mathematics · 2009
In this paper, a new set of generalized Green's relations on a semigroup S, namely the set of Green ♯-relations, are introduced. By using these new Green ♯-relations, we prove that an [Formula: see text]-abundant semigroup is a normal [Formula: see text]-cryptogroup if and only if it is a strong semilattice of completely [Formula: see text]-simple cryptogroups. Our theorem simplifies a construction theorem of normal [Formula: see text]-abundant cryptographs previously described by the authors. Some properties of the good homomorphisms between the normal [Formula: see text]-cryptogroups are also investigated.