Semigroups with complemented congruence lattices (Q1077551)

Using the decomposition of a semigroup into its \({\mathcal J}\)-classes, the paper gives a characterization of all globally idempotent semigroups whose lattice of congruences is complemented. Furthermore, an arbitrary semigroup has a complemented congruence lattice if and only if it is an inflation of a semigroup characterized in this way. Thus the general problem of describing all semigroups with complemented congruence lattices is reduced to that of studying the question for the class of simple semigroups.