Semigroups whose idempotents form a subsemigroup

We prove that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to those of Birget, Margolis and Rhodes, and of Jones and Szendrei on finite E-semigroups. ––– Nous montrons que tout semigroupe S dont les idempotents forment un sous-semigroupe admet un revetement E-unitaire avec la meme propriete. De plus, si S est E-dense ou orthodoxe, alors son revetement peut etre choisi de meme. Enfin, nous decrivons la structure des semigroupes E-unitaires denses. Nos resultats generalisent ceux de Fountain sur les semigroupes dont les idempotents commutent, et sont analogues a ceux de Birget, Margolis et Rhodes et de Jones et Szendrei sur les E-semigroupes finis. ––– Prova-se que todo o semigrupo S cujos idempotentes formam um subsemigrupo admite uma cobertura E-unitaria com a mesma propriedade. Alem disso, se S e E-denso ou regular, entao a sua cobertura pode ser escolhida como sendo do mesmo tipo. Enfim, descreve-se a estrutura dos semigrupos finitos E-unitarios densos. Estes resultados estendem os de Fountain sobre semigrupos cujos idempotentes comutam, e os de Birget, Margolis e Rhodes, e Jones e Szendrei sobre E-semigrupos finitos.

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