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A characterization of left cancellative monoids by flatness properties. S. Bulman-Fleming, k. McDowell (1990) Semigroup forum

A characterization of semigroups which are semilattices of groups S. Lajos (1970) Colloquium Mathematicae

A characterization of semilattices of left or right groups Bedřich Pondělíček (1972) Czechoslovak Mathematical Journal

A class of semigroups having almost trivial multiplications. M. Mislove, J.F. Berglund (1972) Semigroup forum