Regular Cryptic Super r-Ample Semigroups

By utilizing the (*, ͂ )-Green s relations and quasi-strong semilattice of semigroups, we show that a super r-ample semigroup is a regular cryptic super r-ample semigroup if and only if it is a quasi-strong semilattice of completely J* ͂ simple semigroups. This result can be regarded as a generalized result of M. Petrich on normal cryptogroups and regular cryptogroups within the class of regular semigroups to the class of r-ample semigroups.