An H-semigroup is a
semigroup such that every right and every left congruence is a two-sided congruence
on the semigroup. It is known that the set of idempotents of an H-semigroup form a
subsemigroup. A semigroup is t-semisimple provided the intersection of all its
maximal modular congruences is the identity relation. Let S be a periodic
H-semigroup such that the subsemigroup E of idempotents of S is commutative. In
this paper it is shown that S is a semilattice of disjoint one-idempotent
H-semigroups, and that every subgroup of S is a Hamiltonian group. Moreover, if S
is t-semisimple, then S is an inverse semigroup such that the oneridempotent
H-semigroups of the semilattice are the maximal subgroups of S, and a complete
characterization is given.
