Geodesic
Principal quasi-ideals of cohomological dimension~1
Algebra and discrete mathematics, no. 1 (2003), pp. 87-92.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that a principal quasi-ideal of a non-commutative free semigroup has cohomological dimension 1 if and only if it is free.
Keywords: cohomology of semigroups, cohomological dimension, quasi-ideal, free semigroup. 
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B. V. Novikov. Principal quasi-ideals of cohomological dimension~1. Algebra and discrete mathematics, no. 1 (2003), pp. 87-92. http://geodesic.mathdoc.fr/item/ADM_2003_1_a7/