Volume 35 • Number 4 • 2012   • Regular Cryptic Super $r$-Ample Semigroups Kong Xiang-Zhi and Kar Ping Shum Abstract. By utilizing the $(*, \sim)$-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 ${\mathcal{ J}^{*,\sim}}$-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. 2010 Mathematics Subject Classification: 20M10. Full text: PDF