Geodesic
Derivations and relation modules for inverse semigroups
Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 1-19

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We define the derivation module for a homomorphism of inverse semigroups, generalizing a construction for groups due to Crowell. For a presentation map from a free inverse semigroup, we can then define its relation module as the kernel of a canonical map from the derivation module to the augmentation module. The constructions are analogues of the first steps in the Gruenberg resolution obtained from a group presentation. We give a new proof of the characterization of inverse monoids of cohomological dimension zero, and find a class of examples of inverse semigroups of cohomological dimension one.
Keywords: inverse semigroup, cohomology, derivation
Mots-clés : relation module. 
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N. D. Gilbert. Derivations and relation modules for inverse semigroups. Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 1-19. http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a0/