Geodesic
Essential normal and conjugate extensions of inverse semigroups
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 123-130

Voir la notice de l'article provenant de la source Cambridge University Press

In the following we use the notation and terminology of [6] and [7]. If S is an inverse semigroup, then Es denotes the semilattice of idempotents of S. If a is any element of the inverse semigroup, then a−1 denotes the inverse of a in S. An inverse subsemigroup S of an inverse semigroup S′ is self-conjugate in S′ if for all x ∈ S′,x−1Sx ⊆ S; if this is the case, S′ is called a conjugate extension of S. An inverse subsemigroup S of S′ is said to be a full inverse subsemigroup of S′ if Es = Es′. If S is a full self-conjugate inverse subsemigroup of the inverse semigroup S′, then S is called a normal inverse subsemigroup of S′, or, S′ is called a normal extension of S. 
Pastijn, Francis. Essential normal and conjugate extensions of inverse semigroups. Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 123-130. doi: 10.1017/S0017089500004894
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