Derivations and relation modules for inverse semigroups
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 augmentati...
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| Datum: | 2018 |
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-6702018-04-04T09:28:39Z Derivations and relation modules for inverse semigroups Gilbert, N. D. inverse semigroup, cohomology, derivation, relation module 20M18,20M50,18G20 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/670 Algebra and Discrete Mathematics; Vol 12, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/670/204 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-04T09:28:39Z |
| collection |
OJS |
| language |
English |
| topic |
inverse semigroup cohomology derivation relation module 20M18,20M50,18G20 |
| spellingShingle |
inverse semigroup cohomology derivation relation module 20M18,20M50,18G20 Gilbert, N. D. Derivations and relation modules for inverse semigroups |
| topic_facet |
inverse semigroup cohomology derivation relation module 20M18,20M50,18G20 |
| format |
Article |
| author |
Gilbert, N. D. |
| author_facet |
Gilbert, N. D. |
| author_sort |
Gilbert, N. D. |
| title |
Derivations and relation modules for inverse semigroups |
| title_short |
Derivations and relation modules for inverse semigroups |
| title_full |
Derivations and relation modules for inverse semigroups |
| title_fullStr |
Derivations and relation modules for inverse semigroups |
| title_full_unstemmed |
Derivations and relation modules for inverse semigroups |
| title_sort |
derivations and relation modules for inverse semigroups |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/670 |
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AT gilbertnd derivationsandrelationmodulesforinversesemigroups |
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2025-07-17T10:35:36Z |
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2025-07-17T10:35:36Z |
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