Geodesic
The Word Problem for Orthogroups
Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 893-900

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

A semigroup which is a union of groups is said to be completely regular. If in addition the idempotents form a subsemigroup, the semigroup is said to be orthodox and is called an orthogroup. A completely regular semigroup S is provided in a natural way with a unary operation of inverse by letting a -l for a ∈ S be the group inverse of a in the maximal subgroup of S to which a belongs. This unary operation satisfies the identities (1) (2) (3) In fact a completely regular semigroup can be defined as a unary semigroup (a semigroup with an added unary operation) satisfying these identities. An orthogroup can be characterized as a completely regular semigroup satisfying the additional identity (4) 
Gerhard, J. A.; Petrich, Mario. The Word Problem for Orthogroups. Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 893-900. doi: 10.4153/CJM-1981-070-4
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