Semigroups with complemented congruence lattices

Using the decomposition of a semigroup into itsI-classes, the paper gives a characterisation 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 characterised 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.Presented by Boris M. Schein.I wish to thank Professor Schein for his advice to study the work of TuUy ([15]) so that the original version of this paper could be shortened and simplified considerably.