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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154764 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Derivations and relation modules for inverse semigroups / N.D. Gilbert// Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 1–19. — Бібліогр.: 23 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1547642025-02-23T18:48:15Z Derivations and relation modules for inverse semigroups Gilbert, N.D. 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. I am very grateful for constructive email discussions with Benjamin Steinberg andwith Jonathon Funk about this work. 2011 Article Derivations and relation modules for inverse semigroups / N.D. Gilbert// Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 1–19. — Бібліогр.: 23 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20M18,20M50,18G20. https://nasplib.isofts.kiev.ua/handle/123456789/154764 en Algebra and Discrete Mathematics application/pdf Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Gilbert, N.D. |
| spellingShingle |
Gilbert, N.D. Derivations and relation modules for inverse semigroups Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2011 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154764 |
| citation_txt |
Derivations and relation modules for inverse semigroups / N.D. Gilbert// Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 1–19. — Бібліогр.: 23 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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AT gilbertnd derivationsandrelationmodulesforinversesemigroups |
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2025-11-24T11:44:45Z |
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2025-11-24T11:44:45Z |
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