Geodesic
Green's Relations for Regular Elements of Semigroups of Endomorphisms
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1484-1497

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

X is a set and End X is a semigroup, under composition, of functions, which map X into X. We characterize those elements of End X which are regular and then we completely determine Green's relations for these elements. The conditions we place on End X are sufficiently mild to permit such semigroups as S(X), the semigroup of all continuous self maps of a topological space X and L(V), the semigroup of all linear transformations on a vector space V, to be regarded as special cases. 
Jr., K. D. Magill; Subbiah, S. Green's Relations for Regular Elements of Semigroups of Endomorphisms. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1484-1497. doi: 10.4153/CJM-1974-144-x
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