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Algebra and Discrete Mathematics, 2011, Volume 12, Issue 1, Pages 1–19
(Mi adm54)
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This article is cited in 4 scientific papers (total in 4 papers)
RESEARCH ARTICLE
Derivations and relation modules for inverse semigroups
N. D. Gilbert School of Mathematical and Computer Sciences & the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K.
Abstract:
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, relation module.
Received: 23.07.2010 Revised: 10.10.2011
Citation:
N. D. Gilbert, “Derivations and relation modules for inverse semigroups”, Algebra Discrete Math., 12:1 (2011), 1–19
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https://www.mathnet.ru/eng/adm54 https://www.mathnet.ru/eng/adm/v12/i1/p1
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Abstract page: | 200 | Full-text PDF : | 109 | References: | 27 | First page: | 1 |
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