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Semigroups with complemented congruence lattices. (English) Zbl 0595.20066
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.
Reviewer: H.Mitsch

MSC:
20M10 General structure theory for semigroups
20M15 Mappings of semigroups
06B15 Representation theory of lattices
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