$\widetilde{\cal H}$-Supercryptogroups Having Regular Band Congruence
Zhiling Yuan, K. P. Shum · Algebra Colloquium · 2009
We consider a generalized superabundant semigroup within the class of semiabundant semigroups, called a supercryptogroup since it is an analogy of a cryptogroup in the class of regular semigroups. We prove that a semigroup S is an [Formula: see text]-regular supercryptogroup if and only if S can be expressed as a refined semilattice of completely [Formula: see text]-simple semigroups. Some results on regular cryptogroups are extended to [Formula: see text]-regular supercryptogroups. Some results on superabundant semigroups are also generalized.