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Rectangular groupoids and related structures.

Discrete Math, 2013
Boykett T.
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Finitely Generated Idempotent-free Semilattice-Indecomposable Semigroups with Relations I (Algebraic Semigroups, Formal Languages and Computation)

Finitely Generated Idempotent-free Semilattice-Indecomposable Semigroups with Relations I (Algebraic Semigroups, Formal Languages and Computation)
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A class of bisimple, idempotent-generated congruence-free semigroups

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981
SynopsisLet X be a set with infinite regular cardinality m. Within the full transformation semigroup ℑ(X) a subsemigroup Sm is described which is bisimple and idempotent-generated. Its minimum non-trivial homomorphic image has both these properties and is also congruence-free.
J. M. Howie
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The free spectra of varieties generated by idempotent semigroups

2019
We give an exact formula for the logarithm of the free spectra of band varieties.
Pluhar, G., Wood, J.
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Free idempotent generated semigroups: subsemigroups, retracts and maximal subgroups

Communications in Algebra, 2018
Victoria Gould, Thomas Quinn-Gregson
exaly  

Semigroups generated by a group and an idempotent

Communications in Algebra, 1998
Donald B McAlister
exaly  

On regularity and the word problem for free idempotent generated semigroups

Proceedings of the London Mathematical Society, 2017
Igor Dolinka, Nik Ruškuc
exaly  

Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups

Semigroup Forum, 2008
exaly