Characterizing cryptogroups with a finite number of H-classes in each D-class by their subsemigroups
Mario Petrich · 2008
We construct a family F of completely regular semigroups with the prop- erty that each completely regular semigroup S with a finite number of H-classes in each D-class is non-cryptic if and only if S contains an isomorphic image of a member of F. Each member F of F is an ideal extension of a Rees matrix semigroup J by a cyclic group B with a zero adjoined and the identity of B is the identity of F.H ere J = M (I,G, � ;P) with I andfinite, G is given by generators and relations, and P is given explicitly. Within completely regular semigroups, the cryptic property is equivalent to N = S ,w hereN is the natural partial order and aS b if and only if a 2 = ab = ba. Hence the above result can be formulated in terms of N and S.